-
question_answer1)
In a skew symmetric matrix, the diagonal elements are all [MP PET 1987]
A)
Different from each other done
clear
B)
Zero done
clear
C)
One done
clear
D)
None of these done
clear
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question_answer2)
If \[M=\left[ \begin{matrix} 1 & 2 \\ 2 & 3 \\ \end{matrix} \right]\]and \[{{M}^{2}}-\lambda M-{{I}_{2}}=0\], then \[\lambda =\] [MP PET 1990, 2001]
A)
- 2 done
clear
B)
2 done
clear
C)
- 4 done
clear
D)
4 done
clear
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question_answer3)
If \[A=\left[ \begin{matrix} \cos \alpha & -\sin \alpha \\ \sin \alpha & \cos \alpha \\ \end{matrix} \right]\]and \[B=\left[ \begin{matrix} \cos \beta & -\sin \beta \\ \sin \beta & \cos \beta \\ \end{matrix} \right]\], then the correct relation is
A)
\[{{A}^{2}}={{B}^{2}}\] done
clear
B)
\[A+B=B-A\] done
clear
C)
\[AB=BA\] done
clear
D)
None of these done
clear
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question_answer4)
If \[A=\left[ \begin{matrix} 1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 0 & 0 \\ \end{matrix} \right]\], then A is [MP PET 1991]
A)
Symmetric done
clear
B)
Skew-symmetric done
clear
C)
Non-singular done
clear
D)
Singular done
clear
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question_answer5)
If \[A=\left[ \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ a & b & -1 \\ \end{matrix} \right]\], then \[{{A}^{2}}=\] [MNR 1980; Pb. CET 1990; DCE 2001]
A)
Unit matrix done
clear
B)
Null matrix done
clear
C)
A done
clear
D)
- A done
clear
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question_answer6)
If \[A=\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \\ \end{matrix} \right]\], then \[{{A}^{n}}=\] [RPET 1995]
A)
\[\left[ \begin{matrix} 1 & n \\ 0 & 1 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} n & n \\ 0 & n \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} n & 1 \\ 0 & n \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 1 & 1 \\ 0 & n \\ \end{matrix} \right]\] done
clear
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question_answer7)
\[AB=0\], if and only if [MNR 1981; Karnataka CET 1993]
A)
\[A\ne O,B=O\] done
clear
B)
\[A=O,B\ne O\] done
clear
C)
\[A=O\]or \[B=O\] done
clear
D)
None of these done
clear
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question_answer8)
If \[A=\left[ \begin{matrix} 2 & 2 \\ a & b \\ \end{matrix} \right]\]and \[{{A}^{2}}=O\], then \[(a,b)=\]
A)
\[(-2,\,-2)\] done
clear
B)
\[(2,\,-2)\] done
clear
C)
\[(-2,\,2)\] done
clear
D)
\[(2,\,2)\] done
clear
View Solution play_arrow
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question_answer9)
If [m n]\[\left[ \begin{matrix} m \\ n \\ \end{matrix} \right]=[25]\] and m< n, then (m, n) =
A)
(2, 3) done
clear
B)
(3, 4) done
clear
C)
(4, 3) done
clear
D)
None of these done
clear
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question_answer10)
\[A=\left[ \begin{matrix} 4 & 6 & -1 \\ 3 & 0 & 2 \\ 1 & -2 & 5 \\ \end{matrix} \right]\],\[B=\left[ \begin{matrix} 2 & 4 \\ 0 & 1 \\ -1 & 2 \\ \end{matrix} \right],\,\,C=\left[ \begin{matrix} 3 \\ 1 \\ 2 \\ \end{matrix} \right]\], then the expression which is not defined is [MP PET 1987]
A)
\[{{A}^{2}}+2B-2A\] done
clear
B)
\[C{C}'\] done
clear
C)
\[{B}'C\] done
clear
D)
\[AB\] done
clear
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question_answer11)
If \[A=\left[ \begin{matrix} i & 0 \\ 0 & -i \\ \end{matrix} \right],B=\left[ \begin{matrix} 0 & i \\ i & 0 \\ \end{matrix} \right]\], where \[i=\sqrt{-1}\], then the correct relation is
A)
\[A+B=O\] done
clear
B)
\[{{A}^{2}}={{B}^{2}}\] done
clear
C)
\[A-B=O\] done
clear
D)
\[{{A}^{2}}+{{B}^{2}}=O\] done
clear
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question_answer12)
If the matrix \[\left[ \begin{matrix} 1 & 3 & \lambda +2 \\ 2 & 4 & 8 \\ 3 & 5 & 10 \\ \end{matrix} \right]\]is singular, then \[\lambda =\] [MP PET 1990; Pb. CET 2000]
A)
- 2 done
clear
B)
4 done
clear
C)
2 done
clear
D)
- 4 done
clear
View Solution play_arrow
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question_answer13)
If \[A=\left[ \begin{matrix} ab & {{b}^{2}} \\ -{{a}^{2}} & -ab \\ \end{matrix} \right]\]and \[{{A}^{n}}=O\], then the minimum value of n is
A)
2 done
clear
B)
3 done
clear
C)
4 done
clear
D)
5 done
clear
View Solution play_arrow
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question_answer14)
If \[A=\left[ \begin{matrix} 1/3 & 2 \\ 0 & 2x-3 \\ \end{matrix} \right],B=\left[ \begin{matrix} 3 & 6 \\ 0 & -1 \\ \end{matrix} \right]\]and \[AB=I\], then x = [MP PET 1987]
A)
-1 done
clear
B)
1 done
clear
C)
0 done
clear
D)
2 done
clear
View Solution play_arrow
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question_answer15)
If \[AB=C\], then matrices \[A,B,C\]are [MP PET 1991]
A)
\[{{A}_{2\times 3}},{{B}_{3\times 2}},{{C}_{2\times 3}}\] done
clear
B)
\[{{A}_{3\times 2}},{{B}_{2\times 3}},{{C}_{3\times 2}}\] done
clear
C)
\[{{A}_{3\times 3}},{{B}_{2\times 3}},{{C}_{3\times 3}}\] done
clear
D)
\[{{A}_{3\times 2}},{{B}_{2\times 3}},{{C}_{3\times 3}}\] done
clear
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question_answer16)
If \[A=\left[ \begin{matrix} \lambda & 1 \\ -1 & -\lambda \\ \end{matrix} \right]\], then for what value of \[\lambda ,\,{{A}^{2}}=O\] [MP PET 1992]
A)
0 done
clear
B)
\[\pm \text{ }1\] done
clear
C)
- 1 done
clear
D)
1 done
clear
View Solution play_arrow
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question_answer17)
If \[A=\left[ \begin{matrix} 0 & 1 & -2 \\ -1 & 0 & 5 \\ 2 & -5 & 0 \\ \end{matrix} \right]\], then [MNR 1982]
A)
\[{A}'=A\] done
clear
B)
\[{A}'=-A\] done
clear
C)
\[{A}'=2A\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer18)
If \[A=\left[ \begin{matrix} 4 & 1 \\ 3 & 2 \\ \end{matrix} \right]\]and \[I=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\], \[{{A}^{2}}-6A=\] [MP PET 1987]
A)
3I done
clear
B)
5I done
clear
C)
- 5I done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer19)
If \[A=\left[ \begin{matrix} 1 & 2 & 3 \\ 5 & 0 & 7 \\ 6 & 2 & 5 \\ \end{matrix} \right]\]and \[B=\left[ \begin{matrix} 1 & 3 & 5 \\ 0 & 0 & 2 \\ \end{matrix} \right]\], then which of the following is defined
A)
AB done
clear
B)
\[A+B\] done
clear
C)
\[{A}'{B}'\] done
clear
D)
\[{B}'{A}'\] done
clear
View Solution play_arrow
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question_answer20)
If \[A=[1\,\,2\,\text{ }3]\]and \[B=\left[ \begin{matrix} -5 & 4 & 0 \\ 0 & 2 & -1 \\ 1 & -3 & 2 \\ \end{matrix} \right]\], then \[AB=\] [MP PET 1988]
A)
\[\left[ \begin{matrix} -5 & 4 & 0 \\ 0 & 4 & -2 \\ 3 & -9 & 6 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{align} & 3 \\ & 1 \\ & 1 \\ \end{align} \right]\] done
clear
C)
\[\left[ \begin{matrix} -2 & -1 & 4 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} -5 & 8 & 0 \\ 0 & 4 & -3 \\ 1 & -6 & 6 \\ \end{matrix} \right]\] done
clear
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question_answer21)
If A is a \[m\times n\]matrix and B is a matrix such that both AB and BA are defined, then the order of B is
A)
\[m\times n\] done
clear
B)
\[n\times m\] done
clear
C)
\[m\times m\] done
clear
D)
\[n\times n\] done
clear
View Solution play_arrow
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question_answer22)
If \[A=\left[ \begin{align} & 1 \\ & 2 \\ & 3 \\ \end{align} \right],\]then \[A{A}'=\] [MP PET 1992]
A)
14 done
clear
B)
\[\left[ \begin{align} & 1 \\ & 4 \\ & 3 \\ \end{align} \right]\] done
clear
C)
\[\left[ \begin{matrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9 \\ \end{matrix} \right]\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer23)
If \[\left[ \begin{matrix} 2 & -3 \\ 4 & 0 \\ \end{matrix} \right]-\left[ \begin{matrix} a & c \\ b & d \\ \end{matrix} \right]=\left[ \begin{matrix} 1 & 4 \\ 2 & -5 \\ \end{matrix} \right]\], then \[(a,b,c,d)=\]
A)
\[(1,\,6,\,2,\,5)\] done
clear
B)
(1, 2, 7, 5) done
clear
C)
(1, 2, -7, 5) done
clear
D)
(-1, -2, 7, -5) done
clear
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question_answer24)
If \[A=\left[ \begin{matrix} -1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & -1 \\ \end{matrix} \right]\], then \[{{A}^{2}}\]is [MNR 1980]
A)
Null matrix done
clear
B)
Unit matrix done
clear
C)
A done
clear
D)
2A done
clear
View Solution play_arrow
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question_answer25)
If \[A=\left[ \begin{matrix} 0 & 2 & 0 \\ 0 & 0 & 3 \\ -2 & 2 & 0 \\ \end{matrix} \right]\]and \[B=\left[ \begin{matrix} 1 & 2 & 3 \\ 3 & 4 & 5 \\ 5 & -4 & 0 \\ \end{matrix} \right]\], then the element of 3rd row and third column in AB will be
A)
- 18 done
clear
B)
4 done
clear
C)
- 12 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer26)
If \[A=\left[ \begin{matrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \\ \end{matrix} \right],\]then \[{{A}^{5}}=\] [MP PET 1995,1999; Pb. CET 2000]
A)
5A done
clear
B)
10A done
clear
C)
16A done
clear
D)
32A done
clear
View Solution play_arrow
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question_answer27)
If \[A=\left[ \begin{matrix} 0 & 1 \\ 0 & 0 \\ \end{matrix} \right]\]and \[AB=O\], then B = [MP PET 1989]
A)
\[\left[ \begin{matrix} 1 & 1 \\ 1 & 1 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 0 & 1 \\ -1 & 0 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 0 & -1 \\ 1 & 0 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} -1 & 0 \\ 0 & 0 \\ \end{matrix} \right]\] done
clear
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question_answer28)
If A and B are square matrices of order 2, then \[{{(A+B)}^{2}}=\] [MP PET 1992]
A)
\[{{A}^{2}}+2AB+{{B}^{2}}\] done
clear
B)
\[{{A}^{2}}+2AB+{{B}^{2}}\] done
clear
C)
\[{{A}^{2}}+2BA+{{B}^{2}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer29)
If \[A=\left[ \begin{matrix} 1 & 0 & 0 & 0 \\ 2 & 3 & 0 & 0 \\ 4 & 5 & 6 & 0 \\ 7 & 8 & 9 & 10 \\ \end{matrix} \right]\], then A is
A)
An upper triangular matrix done
clear
B)
A null matrix done
clear
C)
A lower triangular matrix done
clear
D)
None of these done
clear
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question_answer30)
Square matrix \[{{[{{a}_{ij}}]}_{n\times n}}\]will be an upper triangular matrix, if
A)
\[{{a}_{ij}}\ne \]0, for \[i>j\] done
clear
B)
\[{{a}_{ij}}\ne \], for \[i>j\] done
clear
C)
\[{{a}_{ij}}=\]0, for \[i<j\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer31)
If the matrix \[\left[ \begin{matrix} 0 & 1 & -2 \\ -1 & 0 & 3 \\ \lambda & -3 & 0 \\ \end{matrix} \right]\]is singular, then \[\lambda \]= [MP PET 1989]
A)
- 2 done
clear
B)
- 1 done
clear
C)
1 done
clear
D)
2 done
clear
View Solution play_arrow
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question_answer32)
Which of the following relations is incorrect
A)
\[(A+B+....+l{)}'={A}'+{B}'+....+{l}'\] done
clear
B)
\[(AB....l{)}'={A}'{B}'....{l}'\] done
clear
C)
\[(kA{)}'=k{A}'\] done
clear
D)
\[(A{)}'=A\] done
clear
View Solution play_arrow
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question_answer33)
If A is a square matrix of order n and \[A=k\]B, where k is a scalar, then |A|= [Karnataka CET 1992]
A)
|B| done
clear
B)
\[k|B|\] done
clear
C)
\[{{k}^{n}}\]|B| done
clear
D)
\[n|B|\] done
clear
View Solution play_arrow
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question_answer34)
If \[A=dig(2,-1,\,3),B=dig(-1,\,3,\,2)\], then \[{{A}^{2}}B=\]
A)
dig (5, 4, 11) done
clear
B)
dig (-4, 3, 18) done
clear
C)
dig (3, 1, 8 ) done
clear
D)
B done
clear
View Solution play_arrow
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question_answer35)
\[\cos \theta \left[ \begin{matrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \\ \end{matrix} \right]+\sin \theta \left[ \begin{matrix} \sin \theta & -\cos \theta \\ \cos \theta & \sin \theta \\ \end{matrix} \right]=\]
A)
\[\left[ \begin{matrix} 0 & 0 \\ 0 & 0 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 1 & 0 \\ 0 & 0 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer36)
If I is a unit matrix, then 3I will be
A)
A unit matrix done
clear
B)
A triangular matrix done
clear
C)
A scalar matrix done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer37)
If \[A=[a\,\,b],B=[-b-a]\]and \[C=\left[ \begin{align} & \,\,\,\,a \\ & -a \\ \end{align} \right]\], then the correct statement is [AMU 1987]
A)
\[A=-B\] done
clear
B)
\[A+B=A-B\] done
clear
C)
\[AC=BC\] done
clear
D)
\[CA=CB\] done
clear
View Solution play_arrow
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question_answer38)
If \[A=\left[ \begin{matrix} 1 & a \\ 0 & 1 \\ \end{matrix} \right]\], then \[{{A}^{4}}\]is equal to [MP PET 1993; Pb. CET 2001]
A)
\[\left[ \begin{matrix} 1 & {{a}^{4}} \\ 0 & 1 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 4 & 4a \\ 0 & 4 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 4 & {{a}^{4}} \\ 0 & 4 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 1 & 4a \\ 0 & 1 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer39)
If \[\left[ \begin{matrix} 3 & 1 \\ 4 & 1 \\ \end{matrix} \right]X=\left[ \begin{matrix} 5 & -1 \\ 2 & 3 \\ \end{matrix} \right],\]then X = [MP PET 1994]
A)
\[\left[ \begin{matrix} -3 & 4 \\ 14 & -13 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 3 & -4 \\ -14 & 13 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 3 & 4 \\ 14 & 13 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} -3 & 4 \\ -14 & 13 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer40)
Which of the following is incorrect
A)
\[{{A}^{2}}-{{B}^{2}}=(A+B)(A-B)\] done
clear
B)
\[{{({{A}^{T}})}^{T}}=A\] done
clear
C)
\[{{(AB)}^{n}}={{A}^{n}}{{B}^{n}},\]where A, B commute done
clear
D)
\[(A-I)(I+A)=O\Leftrightarrow {{A}^{2}}=I\] done
clear
View Solution play_arrow
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question_answer41)
\[A,B\] are n-rowed square matrices such that \[AB=O\]and B is non-singular. Then
A)
\[A\ne O\] done
clear
B)
\[A=O\] done
clear
C)
\[A=I\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer42)
The order of \[[x\,y\,z]\,\,\left[ \begin{matrix} a & h & g \\ h & b & f \\ g & f & c \\ \end{matrix} \right]\,\left[ \begin{align} & x \\ & y \\ & z \\ \end{align} \right]\] is [EAMCET 1994]
A)
\[3\times 1\] done
clear
B)
\[1\times 1\] done
clear
C)
\[1\times 3\] done
clear
D)
\[3\times 3\] done
clear
View Solution play_arrow
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question_answer43)
If A and B are two matrices such that \[AB=B\]and \[BA=A,\] then \[{{A}^{2}}+{{B}^{2}}=\] [EAMCET 1994]
A)
\[2AB\] done
clear
B)
\[2BA\] done
clear
C)
\[A+B\] done
clear
D)
\[AB\] done
clear
View Solution play_arrow
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question_answer44)
If A and B are two matrices and \[(A+B)(A-B)\]\[={{A}^{2}}-{{B}^{2}}\], then [RPET 1995]
A)
\[AB=BA\] done
clear
B)
\[{{A}^{2}}+{{B}^{2}}={{A}^{2}}-{{B}^{2}}\] done
clear
C)
\[{A}'{B}'=AB\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer45)
\[A=\left[ \begin{matrix} 5 & -3 \\ 2 & 4 \\ \end{matrix} \right]\]and \[B=\left[ \begin{matrix} 6 & -4 \\ 3 & 6 \\ \end{matrix} \right],\]then \[A-B=\] [RPET 1995]
A)
\[\left[ \begin{matrix} 11 & -7 \\ 5 & 10 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} -1 & \text{ }1 \\ -1 & -2 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 11 & 7 \\ 5 & -10 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 12 & -7 \\ 5 & -10 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer46)
If \[X=\left[ \begin{matrix} 3 & -4 \\ 1 & -1 \\ \end{matrix} \right]\], then the value of \[{{X}^{n}}\]is [EAMCET 1991]
A)
\[\left[ \begin{matrix} 3n & -4n \\ n & -n \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 2+n & 5-n \\ n & -n \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} {{3}^{n}} & {{(-4)}^{n}} \\ {{1}^{n}} & {{(-1)}^{n}} \\ \end{matrix} \right]\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer47)
If \[A=\left[ \begin{matrix} i & 0 \\ 0 & i \\ \end{matrix} \right]\], then \[{{A}^{2}}=\] [EAMCET 1983]
A)
\[\left[ \begin{matrix} 1 & 0 \\ 0 & -1 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} -1 & 0 \\ 0 & -1 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} -1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer48)
If \[A\] and \[B\] are square matrices of same order, then [Roorkee 1995]
A)
\[A+B=B+A\] done
clear
B)
\[A+B=A-B\] done
clear
C)
\[A-B=B-A\] done
clear
D)
\[AB=BA\] done
clear
View Solution play_arrow
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question_answer49)
If \[A=\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right],\]then \[{{A}^{4}}\]= [EAMCET 1994]
A)
\[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 1 & 1 \\ 0 & 0 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 0 & 0 \\ 1 & 1 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer50)
If \[A=\left[ \begin{matrix} 3 & 1 \\ -1 & 2 \\ \end{matrix} \right]\], then \[{{A}^{2}}=\] [Karnataka CET 1994]
A)
\[\left[ \begin{matrix} 8 & -5 \\ -5 & 3 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 8 & -5 \\ 5 & 3 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 8 & -5 \\ -5 & -3 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 8 & 5 \\ -5 & 3 \\ \end{matrix} \right]\] done
clear
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question_answer51)
If A and B are two matrices such that A+B and AB are both defined, then [Pb. CET 1990]
A)
\[A\]and B are two matrices not necessarily of same order done
clear
B)
A and B are square matrices of same order done
clear
C)
Number of columns of A= Number of rows of B done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer52)
If \[A=\left[ \begin{matrix} 1 & 3 & 0 \\ -1 & 2 & 1 \\ 0 & 0 & 2 \\ \end{matrix} \right],B=\left[ \begin{matrix} 2 & 3 & 4 \\ 1 & 2 & 3 \\ -1 & 1 & 2 \\ \end{matrix} \right]\], then AB = [EAMCET 1987]
A)
\[\left[ \begin{matrix} 5 & 9 & 13 \\ -1 & 2 & 4 \\ -1 & 2 & 4 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 5 & 9 & 13 \\ -1 & 2 & 4 \\ -2 & 2 & 4 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 1 & 2 & 4 \\ -1 & 2 & 4 \\ -2 & 2 & 4 \\ \end{matrix} \right]\] done
clear
D)
None of these done
clear
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question_answer53)
If \[A=\left[ \begin{matrix} 1 & 1 \\ 0 & 1 \\ \end{matrix} \right],\]\[B=\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right],\]then \[AB=\] [EAMCET 1984]
A)
\[\left[ \begin{matrix} 0 & 0 \\ 0 & 0 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 1 & 1 \\ 1 & 0 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
-
question_answer54)
If \[A=\left[ \begin{matrix} i & 0 \\ 0 & i \\ \end{matrix} \right]\] and \[B=\left[ \begin{matrix} 0 & -i \\ -i & 0 \\ \end{matrix} \right]\], then \[(A+B)(A-B)\] is equal to [RPET 1994]
A)
\[{{A}^{2}}-{{B}^{2}}\] done
clear
B)
\[{{A}^{2}}+{{B}^{2}}\] done
clear
C)
\[{{A}^{2}}-{{B}^{2}}+BA+AB\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer55)
If \[A=\left[ \begin{matrix} 1 & -2 \\ 3 & 0 \\ \end{matrix} \right],\] \[B=\left[ \begin{matrix} -1 & 4 \\ 2 & 3 \\ \end{matrix} \right]\], \[C=\left[ \begin{matrix} 0 & -1 \\ 1 & 0 \\ \end{matrix} \right]\], then \[5A-3B-2C\]= [RPET 1992, 94]
A)
\[\left[ \begin{matrix} 8 & 20 \\ 7 & 9 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 8 & -20 \\ 7 & -9 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} -8 & 20 \\ -7 & 9 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 8 & 7 \\ -20 & -9 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
-
question_answer56)
If \[\left[ \begin{matrix} x & 0 \\ 1 & y \\ \end{matrix} \right]+\left[ \begin{matrix} -2 & 1 \\ 3 & 4 \\ \end{matrix} \right]=\left[ \begin{matrix} 3 & 5 \\ 6 & 3 \\ \end{matrix} \right]-\left[ \begin{matrix} 2 & 4 \\ 2 & 1 \\ \end{matrix} \right]\], then [RPET 1994]
A)
\[x=-3,y=-2\] done
clear
B)
\[x=3,y=-2\] done
clear
C)
\[x=3,y=2\] done
clear
D)
\[x=-3,y=2\] done
clear
View Solution play_arrow
-
question_answer57)
If \[A=\left[ \begin{matrix} x & 1 \\ 1 & 0 \\ \end{matrix} \right]\]and \[{{A}^{2}}\] is the identity matrix, then x = [EAMCET 1993]
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
0 done
clear
View Solution play_arrow
-
question_answer58)
If \[A=\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right],B=\left[ \begin{matrix} 0 & -i \\ i & 0 \\ \end{matrix} \right]\] then \[{{(A+B)}^{2}}\]equals [RPET 1994]
A)
\[{{A}^{2}}+{{B}^{2}}\] done
clear
B)
\[{{A}^{2}}+{{B}^{2}}+2AB\] done
clear
C)
\[{{A}^{2}}+{{B}^{2}}+AB-BA\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer59)
If \[A=\left[ \begin{matrix} 0 & 1 \\ 0 & 0 \\ \end{matrix} \right],\]I is the unit matrix of order 2 and a, b are arbitrary constants, then \[{{(aI+bA)}^{2}}\]is equal to [RPET 1992]
A)
\[{{a}^{2}}I+abA\] done
clear
B)
\[{{a}^{2}}I+2abA\] done
clear
C)
\[{{a}^{2}}I+{{b}^{2}}A\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer60)
Matrix theory was introduced by
A)
Newton done
clear
B)
Cayley-Hamilton done
clear
C)
Cauchy done
clear
D)
Euclid done
clear
View Solution play_arrow
-
question_answer61)
If \[A=\left[ \begin{matrix} 1 & 2 \\ -3 & 0 \\ \end{matrix} \right]\]and \[B=\left[ \begin{matrix} -1 & 0 \\ 2 & 3 \\ \end{matrix} \right]\], then [MP PET 1996]
A)
\[{{A}^{2}}=A\] done
clear
B)
\[{{B}^{2}}=B\] done
clear
C)
\[AB\ne BA\] done
clear
D)
\[AB=BA\] done
clear
View Solution play_arrow
-
question_answer62)
Which one of the following is not true [Kurukshetra CEE 1998]
A)
Matrix addition is commutative done
clear
B)
Matrix addition is associative done
clear
C)
Matrix multiplication is commutative done
clear
D)
Matrix multiplication is associative done
clear
View Solution play_arrow
-
question_answer63)
In order that the matrix \[\left[ \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 3 & \lambda & 5 \\ \end{matrix} \right]\] be non-singular, \[\lambda \] should not be equal to [Kurukshetra CEE 1998]
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
View Solution play_arrow
-
question_answer64)
If \[U=[2\,-3\,\,4],X=[0\,\,2\,\,3],\] \[V=\left[ \begin{align} & 3 \\ & 2 \\ & 1 \\ \end{align} \right]\] and \[Y=\left[ \begin{align} & 2 \\ & 2 \\ & 4 \\ \end{align} \right]\], then \[UV+XY\]= [MP PET 1997]
A)
20 done
clear
B)
[- 20] done
clear
C)
- 20 done
clear
D)
[20] done
clear
View Solution play_arrow
-
question_answer65)
If \[A=\left[ \begin{matrix} 0 & i \\ -i & 0 \\ \end{matrix} \right]\], then the value of \[{{A}^{40}}\]is [RPET 1999]
A)
\[\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 1 & 1 \\ 0 & 0 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} -1 & 1 \\ 0 & -1 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
-
question_answer66)
If \[A=\left[ \begin{matrix} 1 & -2 & 1 \\ 2 & 1 & 3 \\ \end{matrix} \right]\] and \[B=\left[ \begin{matrix} 2 & 1 \\ 3 & 2 \\ 1 & 1 \\ \end{matrix} \right]\], then \[{{(AB)}^{T}}=\] [RPET 1996]
A)
\[\left[ \begin{matrix} -3 & -2 \\ 10 & 7 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} -3 & 10 \\ -2 & 7 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} -3 & 10 \\ 7 & -2 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 3 & 10 \\ 2 & 7 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
-
question_answer67)
If \[A=[1\,2\,3],B=\left[ \begin{align} & 2 \\ & 3 \\ & 4 \\ \end{align} \right]\] and \[C=\left[ \begin{matrix} 1 & 5 \\ 0 & 2 \\ \end{matrix} \right]\], then which of the following is defined [RPET 1996]
A)
AB done
clear
B)
\[BA\] done
clear
C)
\[(AB)\,\text{. }C\] done
clear
D)
\[(AC)\,.\,B\] done
clear
View Solution play_arrow
-
question_answer68)
The matrix product \[AB=O\], then [Kurukshetra CEE 1998; RPET 2001]
A)
\[A=O\]and \[B=O\] done
clear
B)
\[A=O\]or \[B=O\] done
clear
C)
A is null matrix done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer69)
If A and B are square matrices of order n × n, then \[{{(A-B)}^{2}}\] is equal to [Karnataka CET 1999; Kerala (Engg.) 2002]
A)
\[{{A}^{2}}-{{B}^{2}}\] done
clear
B)
\[{{A}^{2}}-2AB+{{B}^{2}}\] done
clear
C)
\[{{A}^{2}}+2AB+{{B}^{2}}\] done
clear
D)
\[{{A}^{2}}-AB-BA+{{B}^{2}}\] done
clear
View Solution play_arrow
-
question_answer70)
Choose the correct answer [Karnataka CET 1999]
A)
Every identity matrix is a scalar matrix done
clear
B)
Every scalar matrix is an identity matrix done
clear
C)
Every diagonal matrix is an identity matrix done
clear
D)
A square matrix whose each element is 1 is an identity matrix done
clear
View Solution play_arrow
-
question_answer71)
If \[A=\left[ \begin{matrix} 1 & 0 \\ 2 & 0 \\ \end{matrix} \right],B=\left[ \begin{matrix} 0 & 0 \\ 1 & 12 \\ \end{matrix} \right]\], then [DCE 1999]
A)
\[AB=O,BA=O\] done
clear
B)
\[AB=O,BA\ne O\] done
clear
C)
\[AB\ne O,BA=O\] done
clear
D)
\[AB\ne O,BA\ne O\] done
clear
View Solution play_arrow
-
question_answer72)
The matrix \[\left[ \begin{matrix} 2 & 5 & -7 \\ 0 & 3 & 11 \\ 0 & 0 & 9 \\ \end{matrix} \right]\]is known as [Karnataka CET 1999; Pb. CET 2001]
A)
Symmetric matrix done
clear
B)
Diagonal matrix done
clear
C)
Upper triangular matrix done
clear
D)
Skew symmetric matrix done
clear
View Solution play_arrow
-
question_answer73)
If \[A=\left( \begin{matrix} i & 1 \\ 0 & i \\ \end{matrix} \right)\], then \[{{A}^{4}}\]equals [AMU 1999]
A)
\[\left( \begin{matrix} 1 & -4i \\ 0 & 1 \\ \end{matrix} \right)\] done
clear
B)
\[\left( \begin{matrix} -1 & -4i \\ 0 & -1 \\ \end{matrix} \right)\] done
clear
C)
\[\left( \begin{matrix} -i & 4 \\ 0 & i \\ \end{matrix} \right)\] done
clear
D)
\[\left( \begin{matrix} 1 & 4 \\ 0 & 1 \\ \end{matrix} \right)\] done
clear
View Solution play_arrow
-
question_answer74)
\[\left[ \begin{align} & \,\,\,1 \\ & -1 \\ & \,\,\,2 \\ \end{align} \right]\,\,[2\text{ }1\text{ }-1]\] = [MP PET 2000]
A)
[-1] done
clear
B)
\[\left[ \begin{align} & \,\,\,2 \\ & -1 \\ & -2 \\ \end{align} \right]\] done
clear
C)
\[\left[ \begin{matrix} \,\,2 & \,\,1 & -1 \\ -2 & -1 & \,\,1 \\ \,\,4 & \,\,2 & -2 \\ \end{matrix} \right]\] done
clear
D)
Not defined done
clear
View Solution play_arrow
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question_answer75)
If two matrices A and B are of order p × q and r × s respectively, can be subtracted only, if [RPET 2000]
A)
\[p=q\] done
clear
B)
\[p=q,r=s\] done
clear
C)
\[p=r,q=s\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer76)
If \[A=\left[ \begin{matrix} 1 & 3 \\ 2 & 1 \\ \end{matrix} \right]\], then determinant of \[{{A}^{2}}-2A\]is [EAMCET 2000]
A)
5 done
clear
B)
25 done
clear
C)
-5 done
clear
D)
-25 done
clear
View Solution play_arrow
-
question_answer77)
If the matrix \[AB=O\], then [Pb. CET 2000]
A)
\[A=O\] or \[B=O\] done
clear
B)
\[A=O\] and \[B=O\] done
clear
C)
It is not necessary that either \[A=O\]or \[B=O\] done
clear
D)
\[A\ne O,B\ne O\] done
clear
View Solution play_arrow
-
question_answer78)
If \[{{a}_{ij}}=\frac{1}{2}(3i-2j)\]and \[A={{[{{a}_{ij}}]}_{2\times 2}}\], then A is equal to [RPET 2001]
A)
\[\left[ \begin{matrix} 1/2 & 2 \\ -1/2 & 1 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 1/2 & -1/2 \\ 2 & 1 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 2 & 2 \\ 1/2 & -1/2 \\ \end{matrix} \right]\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer79)
If \[2X-\left[ \begin{matrix} 1 & 2 \\ 7 & 4 \\ \end{matrix} \right]=\left[ \begin{matrix} 3 & 2 \\ 0 & -2 \\ \end{matrix} \right]\], then X is equal to [RPET 2001]
A)
\[\left[ \begin{matrix} 2 & 2 \\ 7 & 4 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 1 & 2 \\ 7/2 & 2 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 2 & 2 \\ 7/2 & 1 \\ \end{matrix} \right]\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer80)
If \[A=\left[ \begin{matrix} 1 & 2 \\ 0 & 1 \\ \end{matrix} \right],\]then \[{{A}^{n}}=\] [Kerala (Engg.) 2001]
A)
\[\left[ \begin{matrix} 1 & 2n \\ 0 & 1 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 2 & n \\ 0 & 1 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 1 & 2n \\ 0 & -1 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 1 & 2n \\ 0 & 1 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
-
question_answer81)
If \[A=\left[ \begin{matrix} 0 & 2 \\ 3 & -4 \\ \end{matrix} \right]\] and \[kA=\left[ \begin{matrix} 0 & 3a \\ 2b & 24 \\ \end{matrix} \right]\], then the values of k, a, b are respectively [EAMCET 2001]
A)
\[-\,6,-\,12,-\,18\] done
clear
B)
- 6, 4, 9 done
clear
C)
\[-\,6,-\,4,-\,9\] done
clear
D)
- 6, 12, 18 done
clear
View Solution play_arrow
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question_answer82)
If \[\left[ \begin{matrix} 2+x & 3 & 4 \\ 1 & -1 & 2 \\ x & 1 & -5 \\ \end{matrix} \right]\]is a singular matrix, then x is [Kerala (Engg.) 2001]
A)
\[\frac{13}{25}\] done
clear
B)
\[-\frac{25}{13}\] done
clear
C)
\[\frac{5}{13}\] done
clear
D)
\[\frac{25}{13}\] done
clear
View Solution play_arrow
-
question_answer83)
For the matrix \[A=\left[ \begin{matrix} 1 & 1 & 0 \\ 1 & 2 & 1 \\ 2 & 1 & 0 \\ \end{matrix} \right]\], which of the following is correct [Kerala (Engg.)2001]
A)
\[{{A}^{3}}+3{{A}^{2}}-I=O\] done
clear
B)
\[{{A}^{3}}-3{{A}^{2}}-I=O\] done
clear
C)
\[{{A}^{3}}+2{{A}^{2}}-I=O\] done
clear
D)
\[{{A}^{3}}-{{A}^{2}}+I=O\] done
clear
View Solution play_arrow
-
question_answer84)
The matrix \[\left[ \begin{matrix} 2 & \lambda & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3 \\ \end{matrix} \right]\]is non singular, if [Kurukshetra CEE 2002]
A)
\[\lambda \ne -2\] done
clear
B)
\[\lambda \ne 2\] done
clear
C)
\[\lambda \ne 3\] done
clear
D)
\[\lambda \ne -3\] done
clear
View Solution play_arrow
-
question_answer85)
If \[A=\left[ \begin{matrix} 1 & -1 \\ 2 & -1 \\ \end{matrix} \right],\,\,B=\left[ \begin{matrix} a & 1 \\ b & -1 \\ \end{matrix} \right]\] and \[{{(A+B)}^{2}}={{A}^{2}}+{{B}^{2}}\], then the value of a and b are [Kurukshetra CEE 2002]
A)
\[a=4,b=1\] done
clear
B)
\[a=1,b=4\] done
clear
C)
\[a=0,b=4\] done
clear
D)
\[a=2,b=4\] done
clear
View Solution play_arrow
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question_answer86)
If \[A,B\]are square matrices of order 3, A is non- singular and \[AB=O\], then B is a [EAMCET 2002]
A)
Null matrix done
clear
B)
Singular matrix done
clear
C)
Unit matrix done
clear
D)
Non- singular matrix done
clear
View Solution play_arrow
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question_answer87)
If \[A=\left[ \begin{matrix} 3 & -5 \\ -4 & 2 \\ \end{matrix} \right],\]then \[{{A}^{2}}-5A=\] [RPET 2002]
A)
I done
clear
B)
14 I done
clear
C)
0 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer88)
If matrix \[A=\left[ \begin{matrix} 0 & -1 \\ 1 & 0 \\ \end{matrix} \right]\], then \[{{A}^{16}}=\][Karnataka CET 2002]
A)
\[\left[ \begin{matrix} 0 & -1 \\ 1 & 0 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} -1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer89)
If \[A=\left[ \begin{matrix} 1 & 1 \\ 1 & 1 \\ \end{matrix} \right],\]then \[{{A}^{100}}=\] [UPSEAT 2002; MP PET 2004]
A)
\[{{2}^{100}}A\] done
clear
B)
\[{{2}^{99}}A\] done
clear
C)
\[{{2}^{101}}A\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer90)
Which is true about matrix multiplication [UPSEAT 2002]
A)
It is commutative done
clear
B)
It is associative done
clear
C)
Both (a) and (b) done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer91)
Matrix \[A=\left[ \begin{matrix} 1 & 0 & -k \\ 2 & 1 & 3 \\ k & 0 & 1 \\ \end{matrix} \right]\]is invertible for [UPSEAT 2002]
A)
\[k=1\] done
clear
B)
\[k=-1\] done
clear
C)
\[k=0\] done
clear
D)
All real k done
clear
View Solution play_arrow
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question_answer92)
If \[\left[ \begin{matrix} x+y & 2x+z \\ x-y & 2z+w \\ \end{matrix} \right]=\left[ \begin{matrix} 4 & 7 \\ 0 & 10 \\ \end{matrix} \right]\], then values of\[x,y,z,w\]are [RPET 2002]
A)
2, 2, 3, 4 done
clear
B)
2, 3, 1, 2 done
clear
C)
3, 3, 0, 1 done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer93)
The value of a for which the matrix \[A=\left( \begin{matrix} a & 2 \\ 2 & 4 \\ \end{matrix} \right)\]is singular if [Kerala (Engg.)2002]
A)
\[a\ne 1\] done
clear
B)
\[a=1\] done
clear
C)
\[a=0\] done
clear
D)
\[a=-1\] done
clear
View Solution play_arrow
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question_answer94)
If \[A=\left( \begin{matrix} 2 & -1 \\ -1 & 2 \\ \end{matrix} \right)\]and I is the unit matrix of order 2, then \[{{A}^{2}}\] equals [Kerala (Engg.) 2002]
A)
\[4A-3I\] done
clear
B)
\[3A-AI\] done
clear
C)
\[A-I\] done
clear
D)
\[A+I\] done
clear
View Solution play_arrow
-
question_answer95)
If \[P=\left( \begin{matrix} i & 0 & -i \\ 0 & -i & i \\ -i & i & 0 \\ \end{matrix} \right)\] and \[Q=\left( \begin{matrix} -i & i \\ 0 & 0 \\ i & -i \\ \end{matrix} \right)\],then \[PQ\] is equal to [Kerala (Engg.) 2002]
A)
\[\left( \begin{matrix} -2 & 2 \\ 1 & -1 \\ 1 & -1 \\ \end{matrix} \right)\] done
clear
B)
\[\left( \begin{matrix} \,2 & -2 \\ -1 & \,\,\,1 \\ -1 & \,\,\,1 \\ \end{matrix} \right)\] done
clear
C)
\[\left( \begin{matrix} 2 & -2 \\ -1 & \,\,1 \\ \end{matrix} \right)\] done
clear
D)
\[\left( \begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{matrix} \right)\] done
clear
View Solution play_arrow
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question_answer96)
If I is a unit matrix of order 10, then the determinant of I is equal to [Kerala (Engg.) 2002]
A)
10 done
clear
B)
1 done
clear
C)
1/10 done
clear
D)
9 done
clear
View Solution play_arrow
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question_answer97)
Assuming that the sums and products given below are defined, which of the following is not true for matrices [Karnataka CET 2003]
A)
\[A+B=B+A\] done
clear
B)
\[AB=AC\]does not imply \[B=C\] done
clear
C)
\[AB=O\]implies \[A=O\]or \[B=O\] done
clear
D)
\[(AB{)}'={B}'{A}'\] done
clear
View Solution play_arrow
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question_answer98)
If \[A=\left[ \begin{matrix} 1 & 2 & -1 \\ 3 & 0 & \,\,2 \\ 4 & 5 & \,\,0 \\ \end{matrix} \right]\], \[B=\left[ \begin{matrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 0 & 1 & 3 \\ \end{matrix} \right],\]then \[AB\] is [MP PET 2003]
A)
\[\left[ \begin{matrix} 5 & 1 & -3 \\ 3 & 2 & 6 \\ 14 & 5 & 0 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 11 & 4 & 3 \\ 1 & 2 & 3 \\ 0 & 3 & 3 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 1 & 8 & 4 \\ 2 & 9 & 6 \\ 0 & 2 & 0 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 0 & 1 & 2 \\ 5 & 4 & 3 \\ 1 & 8 & 2 \\ \end{matrix} \right]\] done
clear
View Solution play_arrow
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question_answer99)
If A and B are \[3\times 3\]matrices such that \[AB=A\] and \[BA=B\], then [Orissa JEE 2003]
A)
\[{{A}^{2}}=A\]and \[{{B}^{2}}\ne B\] done
clear
B)
\[{{A}^{2}}\ne A\]and \[{{B}^{2}}=B\] done
clear
C)
\[{{A}^{2}}=A\]and \[{{B}^{2}}=B\] done
clear
D)
\[{{A}^{2}}\ne A\]and \[{{B}^{2}}\ne B\] done
clear
View Solution play_arrow
-
question_answer100)
If \[A=\left[ \begin{matrix} \alpha & 0 \\ 1 & 1 \\ \end{matrix} \right]\]and \[B=\left[ \begin{matrix} 1 & 0 \\ 5 & 1 \\ \end{matrix} \right]\], then value of\[\alpha \]for which \[{{A}^{2}}=B\], is [IIT Screening 2003]
A)
1 done
clear
B)
-1 done
clear
C)
4 done
clear
D)
No real values done
clear
View Solution play_arrow
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question_answer101)
\[\left[ \begin{matrix}
7 & 1 & 2 \\
9 & 2 & 1 \\
\end{matrix} \right]\left[ \begin{matrix}
3 \\
4 \\
5 \\
\end{matrix} \right]+2\left[ \begin{matrix}
4 \\
2 \\
\end{matrix} \right]\]
is equal to [DCE 2002]
A)
\[\left[ \begin{align} & 43 \\ & 44 \\ \end{align} \right]\] done
clear
B)
\[\left[ \begin{align} & 43 \\ & 45 \\ \end{align} \right]\] done
clear
C)
\[\left[ \begin{align} & 45 \\ & 44 \\ \end{align} \right]\] done
clear
D)
\[\left[ \begin{align} & 44 \\ & 45 \\ \end{align} \right]\] done
clear
View Solution play_arrow
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question_answer102)
Let \[A=\left( \begin{matrix} 0 & 0 & -1 \\ 0 & -1 & 0 \\ -1 & 0 & 0 \\ \end{matrix} \right)\], the only correct statement about the matrix A is [AIEEE 2004]
A)
\[{{A}^{2}}=I\] done
clear
B)
\[A=(-1)\,I,\]where I is a unit matrix done
clear
C)
\[{{A}^{-1}}\]does not exist done
clear
D)
A is a zero matrix done
clear
View Solution play_arrow
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question_answer103)
If \[A=\left( \begin{matrix} 1 & 2 & 3 \\ 3 & 1 & 2 \\ 2 & 3 & 1 \\ \end{matrix} \right)\] and \[B=\left( \begin{matrix} -5 & 7 & 1 \\ 1 & -5 & 7 \\ 7 & 1 & -5 \\ \end{matrix} \right)\] then \[AB\] is equal to [Pb. CET 2002]
A)
\[{{I}_{3}}\] done
clear
B)
\[2{{I}_{3}}\] done
clear
C)
\[4{{I}_{3}}\] done
clear
D)
\[18{{I}_{3}}\] done
clear
View Solution play_arrow
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question_answer104)
What must be the matrix X if \[2X+\left[ \begin{matrix} 1 & 2 \\ 3 & 4 \\ \end{matrix} \right]=\left[ \begin{matrix} 3 & 8 \\ 7 & 2 \\ \end{matrix} \right]\] [Karnataka CET 2004]
A)
\[\left[ \begin{matrix} 1 & 3 \\ 2 & -1 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 1 & -3 \\ 2 & -1 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 2 & 6 \\ 4 & -2 \\ \end{matrix} \right]\] done
clear
D)
\[\left[ \begin{matrix} 2 & -6 \\ 4 & -2 \\ \end{matrix} \right]\] done
clear
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question_answer105)
If \[A+B=\left[ \begin{matrix} 1 & 0 \\ 1 & 1 \\ \end{matrix} \right]\]and \[A-2B=\left[ \begin{matrix} -1 & 1 \\ 0 & -1 \\ \end{matrix} \right]\,,\]then A= [Karnataka CET 1994]
A)
\[\left[ \begin{matrix} 1 & 1 \\ 2 & 1 \\ \end{matrix} \right]\] done
clear
B)
\[\left[ \begin{matrix} 2/3 & 1/3 \\ 1/3 & 2/3 \\ \end{matrix} \right]\] done
clear
C)
\[\left[ \begin{matrix} 1/3 & 1/3 \\ 2/3 & 1/3 \\ \end{matrix} \right]\] done
clear
D)
None of these done
clear
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question_answer106)
The identity element in the group \[M=\left\{ \left. \left( \begin{matrix} x & x \\ x & x \\ \end{matrix} \right) \right|x\in R;\,x\ne 0\, \right\}\] with respect to matrix multiplication is [Karnataka CET 2005]
A)
\[\left( \begin{matrix} 1 & 1 \\ 1 & 1 \\ \end{matrix} \right)\] done
clear
B)
\[\frac{1}{2}\left( \begin{matrix} 1 & 1 \\ 1 & 1 \\ \end{matrix} \right)\] done
clear
C)
\[\left( \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right)\] done
clear
D)
\[\left( \begin{matrix} 0 & 1 \\ 1 & 0 \\ \end{matrix} \right)\] done
clear
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question_answer107)
If \[A=\left[ \begin{matrix} 1 & 0 \\ 1 & 1 \\ \end{matrix} \right]\] and \[I=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\], then which one of the following holds for all \[n\ge 1\], (by the principal of mathematical induction) [AIEEE 2005]
A)
\[{{A}^{n}}=nA+(n-1)I\] done
clear
B)
\[{{A}^{n}}={{2}^{n-1}}A+(n-1)I\] done
clear
C)
\[{{A}^{n}}=nA-(n-1)I\] done
clear
D)
\[{{A}^{n}}={{2}^{n-1}}A-(n-1)I\] done
clear
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