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question_answer1) If \[A=\left[ \begin{matrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \\ \end{matrix} \right],\] then the matrix \[{{A}^{-50}}\] when \[\theta =\frac{\pi }{12},\] is equal to \[\left[ \begin{matrix} a & b \\ c & d \\ \end{matrix} \right],\] then the value of \[a+b+c-d\] is
question_answer2) Let \[A=\left( \begin{matrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \\ \end{matrix} \right)\] and \[10\,B=\left( \begin{matrix} 4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3 \\ \end{matrix} \right).\] If B is the inverse of matrix A, then \[\alpha \] is
question_answer3) The number of \[3\times 3\] matrices M with entries from \[\{0,1,2\}\] for which the sum of the diagonal entries of \[{{M}^{T}}M\] is \[5,\]are
question_answer4) Let \[P=\left[ \begin{matrix} 1 & 0 & 0 \\ 3 & 1 & 0 \\ 9 & 3 & 1 \\ \end{matrix} \right]\] and \[Q=[{{q}_{ij}}]\]be two \[3\times 3\] matrices such that \[Q-{{P}^{5}}={{I}_{3}}.\] Then \[\frac{{{q}_{21}}+{{q}_{31}}}{{{q}_{32}}}\] is equal to
question_answer5) If \[A=\left[ \begin{matrix} x & 1 \\ 1 & 0 \\ \end{matrix} \right]\] and \[{{A}^{2}}\] is the unit matrix, then the value of \[{{x}^{3}}+x+2\] is equal to
question_answer6) If \[f(x)={{x}^{2}}+4x-5\] and \[A=\left[ \begin{matrix} 1 & 2 \\ 4 & -3 \\ \end{matrix} \right],\] then the sum of all elements of \[f(A)\] is equal to
question_answer7) Let \[(\alpha \in R)\] such that . If the value of \[\alpha \] is \[\frac{\pi }{{{2}^{k}}},\] then the value of k is
question_answer8) If then x=
question_answer9) If and then the element of third row and third column in AB will be
question_answer10) The total number of matrices \[(x,y\in R,\,x\ne y)\] for which \[{{A}^{T}}A=3{{I}_{3}}\] is:
question_answer11) If is symmetric, then x=
question_answer12) If and then the number of value of \[\alpha \] for which \[{{A}^{2}}=B,\] is
question_answer13) If and \[{{A}^{100}}={{2}^{k}}A,\] then the value of k is
question_answer14) If and \[{{A}^{n}}=O,\] then the minimum value of n is
question_answer15) The total number of matrices \[(x,y\in R,\,\,x\ne y)\] for which \[{{A}^{T}}A=3{{I}_{3}}\] is
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