CBSE Questions for Class 12 Commerce Maths Matrices Quiz 12 - MCQExams.com

If $$A=\left[ \begin{matrix} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{matrix} \right] $$, then $$A^{2}-4\ A$$ is equal to
  • $$2\ I_3$$
  • $$3\ I_3$$
  • $$4\ I_3$$
  • $$5\ I_3$$
If $$A$$ and $$B$$ are square matrices such that $$B=-A^{-1}BA$$, then 
  • $$AB+BA=0$$
  • $$(A+B)^{o}=A^{2}+B^{2}$$
  • $$(A+B)^{2}=A^{2}+2AB+B^{2}$$
  • $$(A+B)^{2}=A+B$$
If $$A=\left[ \begin{matrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{matrix} \right] $$ and $$10B=\left[ \begin{matrix} 4 & 2 & 2 \\ -5 & 0 & \alpha  \\ 1 & -2 & 3 \end{matrix} \right] $$ where $$B=A^{-1}$$ then $$\alpha$$ is equal to-
  • $$2$$
  • $$-1$$
  • $$-2$$
  • $$5$$
The inverse of the matrix  $$\left[ \begin{array} { c c c } { 1 } & { 0 } & { 0 } \\ { 3 } & { 3 } & { 0 } \\ { 5 } & { 2 } & { - 1 } \end{array} \right]$$  is
  • $$- \dfrac { 1 } { 3 } \left[ \begin{array} { c c c } { - 3 } & { 0 } & { 0 } \\ { 3 } & { 1 } & { 0 } \\ { 9 } & { 2 } & { - 3 } \end{array} \right]$$
  • $$- \dfrac { 1 } { 3 } \left[ \begin{array} { c c c } { - 3 } & { 0 } & { 0 } \\ { 3 } & { - 1 } & { 0 } \\ { - 9 } & { - 2 } & { 3 } \end{array} \right]$$
  • $$- \dfrac { 1 } { 3 } \left[ \begin{array} { c c c } { 3 } & { 0 } & { 0 } \\ { 3 } & { - 1 } & { 0 } \\ { - 9 } & { - 2 } & { 3 } \end{array} \right]$$
  • $$- \dfrac { 1 } { 3 } \left[ \begin{array} { c c c } { - 3 } & { 0 } & { 0 } \\ { - 3 } & { - 1 } & { 0 } \\ { - 9 } & { - 2 } & { 3 } \end{array} \right]$$
If $$A$$ is a $$2\times 2$$ matrix such that $$A^{2}-4A+3I=0$$, then the inverse of $$A+3I$$ is equal to
  • $$\dfrac{1}{24}S-\dfrac{7}{24}I$$
  • $$\dfrac{1}{21} A-\dfrac{7}{21}I$$
  • $$\dfrac{7}{24}I+\dfrac{1}{24}A$$
  • $$A-3I$$`
Let A be a $$3\times 3$$ matrix such that
$$A\left[ \begin{matrix} 1 & 2 & 3 \\ 0 & 2 & 3 \\ 0 & 1 & 1 \end{matrix} \right] =\left[ \begin{matrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{matrix} \right] $$  Then $${ A }^{ -1 }$$.
  • $$\left[ \begin{matrix} 1 & 2 & 3 \\ 0 & 1 & 1 \\ 0 & 2 & 3 \end{matrix} \right] $$
  • $$\left[ \begin{matrix} 3 & 1 & 2 \\ 3 & 0 & 2 \\ 1 & 0 & 1 \end{matrix} \right] $$
  • $$\left[ \begin{matrix} 3 & 2 & 1 \\ 3 & 2 & 0 \\ 1 & 1 & 0 \end{matrix} \right] $$
  • $$\left[ \begin{matrix} 0 & 1 & 3 \\ 0 & 2 & 3 \\ 1 & 1 & 1 \end{matrix} \right] $$
Inverse of $$\begin{bmatrix} -1 & 5 \\ -3 & 2 \end{bmatrix}$$ is
  • $$\begin{bmatrix} 2/13 & -5/13 \\ 3/13 & -1/13 \end{bmatrix}$$
  • $$\begin{bmatrix} -2/13 & 5/13 \\ -3/13 & 1/13 \end{bmatrix}$$
  • $$\begin{bmatrix} 2 & -5 \\ 3 & -1 \end{bmatrix}$$
  • $$Cannot\ be\ determined$$
If $$A=\left[ \begin{matrix} cos\theta  & -sin\theta  \\ sin\theta  & cos\theta  \end{matrix} \right] { A }^{ 1 }$$ is given by:
  • $$-A$$
  • $${ A }^{ 1 }$$
  • $${ -A }^{ 1 }$$
  • $$A$$
If $$\begin{bmatrix} 1 & -\tan { \theta  }  \\ \tan { \theta  }  & 1 \end{bmatrix}{ \begin{bmatrix} 1 & -\tan { \theta  }  \\ \tan { \theta  }  & 1 \end{bmatrix} }^{ -1 }={ \begin{bmatrix} \cos { \alpha  }  & -\sin { \alpha  }  \\ \sin { \alpha  }  & \cos { \alpha  }  \end{bmatrix} }^{ -1 }$$, then $$\alpha $$=
  • $$0$$
  • $$\frac { \pi }{ 2 } $$
  • $$\frac { \pi }{ 4 } $$
  • $$\frac { \pi }{ 6 } $$
A is a $$2\times 2$$ matrix such that $$A\begin{bmatrix} 1 &  \\  & -1 \end{bmatrix}=\begin{bmatrix} 1 &  \\ 0 &  \end{bmatrix}$$ and $${ A }^{ 2 }\begin{bmatrix} 1 &  \\  & -1 \end{bmatrix}=\begin{bmatrix} 1 &  \\ 0 &  \end{bmatrix}$$. The sum of the elements f A, is
  • -1
  • 0
  • 2
  • 5
Let A be a $$3 \times 3$$  matrix such that is: $$A\left[ \begin{matrix} 1 & 2 & 3 \\ 0 & 2 & 3 \\ 0 & 1 & 1 \end{matrix} \right]=\left[ \begin{matrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{matrix} \right]  $$Then $$A^{-1}$$ is
  • $$\left[ \begin{matrix} 0 & 1 & 3 \\ 0 & 2 & 3 \\ 1 & 1 & 1 \end{matrix} \right] $$
  • $$\left[ \begin{matrix} 3 & 2 & 1 \\ 3 & 2 & 0 \\ 1 & 1 & 0 \end{matrix} \right] $$
  • $$\left[ \begin{matrix} 1 & 2 & 3 \\ 0 & 1 & 1 \\ 0 & 2 & 3 \end{matrix} \right] $$
  • $$\left[ \begin{matrix} 3 & 1 & 2 \\ 3 & 0 & 2 \\ 1 & 0 & 1 \end{matrix} \right] $$
If $$A=[x \quad y],B=[_{ h } ^{ a }\quad _{ b } ^{ h }],C=[_{ y } ^{ x }]$$, then $$ABC = $$ ___.
  • $$({ ax }+hy+{ bxy })$$
  • $$({ ax }^{ 2 }+2hxy+{ by }^{ 2 })$$
  • $$({ ax }^{ 2 }-2hxy+{ by }^{ 2 })$$
  • $$({ bx }^{ 2 }-2hxy+{ ay }^{ 2 })$$
If $$A=\begin{bmatrix} \alpha  & 0 \\ 1 & 1 \end{bmatrix}$$ and $$B=\begin{bmatrix} 1 & 0 \\ 5 & 1 \end{bmatrix}$$ then the value of $$\alpha $$ for which $$A^2=b$$ is
  • 1
  • -1
  • 4
  • no real value
If a , b and c are all different from zero such that $$\dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c} = 0$$, then the matrix A = $$\begin{vmatrix} 1 + a & 1 & 1 \\ 1 & 1 + b & 1 \\ 1 & 1 & 1 + c \end{vmatrix}$$ is - 
  • symmetric
  • non-singular
  • can be written as sum of a symmetric and a skew symmetric matrix
  • none of these
If $$\displaystyle \begin{bmatrix} a & b \\ -a & 2b \end{bmatrix}\left[ \begin{matrix} 2 \\ -1 \end{matrix} \right] =\left[ \begin{matrix} 5 \\ 4 \end{matrix} \right] $$ then $$(a,b)$$ is
  • $$(1,-3)$$
  • $$(-3,1)$$
  • $$(1,3)$$
  • $$(-1,3)$$
Matrix A when multiplied with Matrix C gives the Identity matrix I, what is C?
  • Identity matrix
  • Inverse of A
  • Square of A
  • Transpose of A
For each real $$ x, -1 < x < 1 . $$ let A (x) be the matrix $$(1-x)^{-1} \begin{bmatrix} 1 & -x \\ -x & 1 \end{bmatrix} $$ and  z  = $$ \dfrac { x +y }{ 1 +xy} $$. then 
  • $$ A (z) = A(x) A(y) $$
  • $$ A (z) = A(x) - A(y) $$
  • $$ A(z) = A(x) + A(y ) $$
  • $$ A(z) = A(x) [ A (y)]^{-1} $$
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