JEE Main & Advanced Mathematics Determinants & Matrices Question Bank

done Numerical Value Type Questions - Matrix Total Questions - 15

• question_answer1)
  If three matrices  Then
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• question_answer2)
  If A is a square matrix of order 3 such that , then find \[\left| adj.A \right|.\] 
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• question_answer3)
  If \[{{A}^{2}}=A\] and \[{{\left( I+A \right)}^{4}}\] is equal to \[I+kA\] then find k.
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• question_answer4)
  If and \[C=5A,\]the find\[\frac{\left| adj\,\,B \right|}{\left| C \right|}\].
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• question_answer5)
  If and \[UV+XY=\left[ k \right]\]then find k.
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• question_answer6)
  If A is a square matrix of order n such that \[\left| adj\,\left( adj\,\,A \right)\, \right|={{\left| A \right|}^{9}},\]then find the value of n.
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• question_answer7)
  If \[P=\left[ \begin{matrix}    \frac{\sqrt{3}}{2} & \frac{1}{2}  \\    -\frac{1}{2} & \frac{\sqrt{3}}{2}  \\ \end{matrix} \right],A=\left[ \begin{matrix}    1 & 1  \\    0 & 1  \\ \end{matrix} \right],Q=PA{{P}^{T}}\]and \[{{P}^{T}}{{Q}^{2005}}P=\left[ \begin{matrix}    1 & k  \\    0 & 1  \\ \end{matrix} \right]\] then find k.
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• question_answer8)
  If  and I is a unit matrix of 3rd order then find the element \[{{a}_{22}}\]of\[\left( {{A}^{2}}+9I \right)\].
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• question_answer9)
  In a symmetric matrix of order '12' find maximum number of different elements.
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• question_answer10)
  A is a \[2\times 2\] matrix such thatand find the sum of the elements of A.
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• question_answer11)
  Let and \[\left| A \right|=1,\,\,abc=1,\]then find the value of\[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}\].
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• question_answer12)
  Find the sum of the values of x satisfying the equation
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• question_answer13)
  If \[A=\left[ \begin{matrix}    1 & 1  \\    1 & 1  \\ \end{matrix} \right]\] and \[{{A}^{100}}\] is equal to \[{{2}^{k}}A\] then find k.
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• question_answer14)
  If \[A=\left[ \begin{matrix}    1 & 2 & -1  \\    -1 & 1 & 2  \\    2 & -1 & 1  \\ \end{matrix} \right]\] and det \[\left[ adj\,\,A \right]\] is equal to \[{{k}^{\lambda }}\] then find \[\left( k+\lambda  \right)\].
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• question_answer15)
  The number of different matrices can be formed using 12 different real numbers is \[m\left( 12 \right)!\] then find the value of m.  
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