CBSE Questions for Class 12 Commerce Maths Matrices Quiz 8 - MCQExams.com

If $$A$$ is a scalar matrix $$kI$$ with scalar $$k\ne 0$$ of order $$3$$, the $${A}^{-1}$$ is:
  • $$\cfrac { 1 }{ { k }^{ 2 } } I$$
  • $$\cfrac { 1 }{ { k }^{ 3 } } I$$
  • $$\cfrac { 1 }{ { k}^{ } } I$$
  • $$kI$$
If $$A=\begin{bmatrix} 7 & 2 \\ 1 & 3 \end{bmatrix}$$ and $$A+B=\begin{bmatrix} -1 & 0 \\ 2 & -4 \end{bmatrix},$$ then matrix $$B=$$?
  • $$\begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix}$$
  • $$\begin{bmatrix} 6 & 2 \\ 3 & -1 \end{bmatrix}$$
  • $$\begin{bmatrix} -8 & -2 \\ 1 & -7 \end{bmatrix}$$
  • $$\begin{bmatrix} 8 & 2 \\ -1 & 7 \end{bmatrix}$$
If $$A = \begin{bmatrix} 4& -2\\ 6 & -3\end{bmatrix}$$, then $$A^2$$ is
  • $$\begin{bmatrix} 16 & 4\\ 36 & 9\end{bmatrix}$$
  • $$\begin{bmatrix} 8 & -4\\ 12 & -6\end{bmatrix}$$
  • $$\begin{bmatrix} -4 & 2\\ -6 & 3\end{bmatrix}$$
  • $$\begin{bmatrix} 4 & -2\\ 6 & -3\end{bmatrix}$$
If $$A+B=\begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix}$$ and $$A=\begin{bmatrix} 1 & 2 \\ 0 & 3 \end{bmatrix}$$, then matrix $$B$$ is
  • $$\begin{bmatrix} 1 & 1 \\ 4 & 2 \end{bmatrix}$$
  • $$\begin{bmatrix} 1 & 4 \\ 1 & 2 \end{bmatrix}$$
  • $$\begin{bmatrix} 2 & 4 \\ 1 & 1 \end{bmatrix}$$
  • $$\begin{bmatrix} 4 & 2 \\ 1 & 1 \end{bmatrix}$$
If $$\bigl(\begin{smallmatrix} 1& 2\\ 2 & 1\end{smallmatrix}\bigr) \bigl(\begin{smallmatrix} x \\ y \end{smallmatrix}\bigr) = \bigl(\begin{smallmatrix} 2 \\  4 \end{smallmatrix}\bigr)$$, then the values of $$x$$ and $$y$$ respectively, are
  • $$2, 0$$
  • $$0, 2$$
  • $$0, -2$$
  • $$1, 1$$
If $$\begin{bmatrix} 5 & x & 1 \end{bmatrix} \begin{bmatrix} 2 \\ -1 \\ 3 \end{bmatrix}  = (20)$$, then the value of $$x$$ is
  • $$7$$
  • $$-7$$
  • $$\dfrac{1}{7}$$
  • $$0$$
If $$A = \begin{bmatrix}7 &2 \\ 1 & 3\end{bmatrix}$$ and $$A + B = \begin{bmatrix} -1& 0\\ 2 & -4\end{bmatrix}$$, then the matrix $$B =$$
  • $$\left[\begin{matrix}1 &0 \\ 0 & 1\end{matrix}\right]$$
  • $$\left[\begin{matrix} 6&2 \\ 3 & -1\end{matrix}\right]$$
  • $$\left[\begin{matrix} -8& -2\\ 1 & -7\end{matrix}\right]$$
  • $$\left[\begin{matrix} 8& 2\\ -1 & 7\end{matrix}\right]$$
Choose the correct statement related to the matrices $$A=\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}$$ and $$B=\begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}$$
  • $$A^3=A, B^3 \ne B$$
  • $$A^3\ne A, B^3=B$$
  • $$A^3=A, B^3 = B$$
  • $$A^3\ne A, B^3 \ne B$$
If $$A = \bigl(\begin{smallmatrix} 4& -2\\ 6 & -3\end{smallmatrix}\bigr)$$, then $$A^2$$ is
  • $$\bigl(\begin{smallmatrix} 16 & 4\\ 36 & 9\end{smallmatrix}\bigr)$$
  • $$\bigl(\begin{smallmatrix}8 & -4\\ 12 & -6\end{smallmatrix}\bigr)$$
  • $$\bigl(\begin{smallmatrix} -4& 2\\ -6 & 3\end{smallmatrix}\bigr)$$
  • $$\bigl(\begin{smallmatrix} 4& -2\\ 6 & -3\end{smallmatrix}\bigr)$$
$$\bigl(\begin{smallmatrix} -1& 0\\ 0 & 1\end{smallmatrix}\bigr) \bigl(\begin{smallmatrix}a & b\\ c & d\end{smallmatrix}\bigr) = \bigl(\begin{smallmatrix} 1& 0\\ 0 & -1\end{smallmatrix}\bigr)$$, then the values of $$a, b, c $$ and $$d $$ respectively are
  • $$-1, 0, 0, -1$$
  • $$1, 0, 0, 1$$
  • $$-1, 0, 1, 0$$
  • $$1, 0, 0, 0$$
If $$\bigl(\begin{smallmatrix}a & 3\\ 1 & 2\end{smallmatrix}\bigr) \bigl(\begin{smallmatrix} 2 \\ -1 \end{smallmatrix}\bigr) = \bigl(\begin{smallmatrix} 5\\ 0 \end{smallmatrix}\bigr)$$, then the value of $$a$$ is
  • $$8$$
  • $$4$$
  • $$2$$
  • $$11$$
If $$A=\left[ \begin{matrix} 1 & -2 & 3 \end{matrix} \right] $$ and $$B=\left[ \begin{matrix} -1 \\ 2 \\ -3 \end{matrix} \right] $$, then $$A + B$$ is
  • $$\begin{bmatrix} 0& 0 & 0 \end{bmatrix}$$
  • $$\begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}$$
  • $$\begin{bmatrix} -1& 4 \end{bmatrix}$$
  • not defined
If matrix $$A=\begin{bmatrix} 1 & 2 \\ 4 & 3 \end{bmatrix}$$ such that $$Ax=I$$, then $$x=$$................
  • $$\cfrac { 1 }{ 5 } \begin{bmatrix} 1 & 3 \\ 2 & -1 \end{bmatrix}$$
  • $$\cfrac { 1 }{ 5 } \begin{bmatrix} 4 & 2 \\ 4 & -1 \end{bmatrix}$$
  • $$\cfrac { 1 }{ 5 } \begin{bmatrix} -3 & 2 \\ 4 & -1 \end{bmatrix}$$
  • $$\cfrac { 1 }{ 5 } \begin{bmatrix} -1 & 2 \\ -1 & 4 \end{bmatrix}$$
The matrix $$A = \begin{bmatrix} 0& 1 & -1\\ -1 & 0 & 1\\ 1 & -1 & 0\end{bmatrix}$$ is a :
  • Diagonal matrix
  • Symmetric matrix
  • Skew-symmetric matrix
  • Identity matrix
The inverse of a diagonal matrix is a :
  • Symmetric matrix
  • Skew-symmetric matrix
  • Diagonal matrix
  • None of the above
If $$\begin{bmatrix} 3 & -1 \\ 0 & 6 \end{bmatrix}\begin{bmatrix} 3x \\ 1 \end{bmatrix}+\begin{bmatrix} -2x \\ 3 \end{bmatrix}=\begin{bmatrix} 8 \\ 9 \end{bmatrix}$$, then the value of $$x$$ is
  • $$-\dfrac { 3 }{ 8 } $$
  • $$7$$
  • $$-\dfrac { 2 }{ 9 } $$
  • None of these
Let $$A = \begin{bmatrix}x + y & y\\ 2x & x - y\end{bmatrix}, B = \begin{bmatrix} 2& -1\end{bmatrix}$$ and $$C = \begin{bmatrix} 3& 2\end{bmatrix}.$$ If $$AB = C$$, then $$A^{2}$$ is equal to
  • $$\begin{bmatrix}

    6 & -10\\

    4 & 26

    \end{bmatrix}$$
  • $$\begin{bmatrix}

    -10 & 5\\

    4 & 24

    \end{bmatrix}$$
  • $$\begin{bmatrix}

    -5 & -6\\

    -4 & -20

    \end{bmatrix}$$
  • None of these.
If the matrix A is such that $$\begin{bmatrix} 1 & 3\\ 0 & 1\end{bmatrix} A=\begin{bmatrix} 1 & 1 \\ 0 & -1\end{bmatrix}$$, then what is equal to A?
  • $$\begin{bmatrix} 1 & 4 \\ 0 & -1\end{bmatrix}$$
  • $$\begin{bmatrix} 1 & 4 \\ 0 & 1\end{bmatrix}$$
  • $$\begin{bmatrix} -1 & 4\\ 0 & -1\end{bmatrix}$$
  • $$\begin{bmatrix} 1 & -4 \\ 0 & -1\end{bmatrix}$$
If $$A=\begin{bmatrix}1&1&-1\\2&-3&4\\3&-2&3\end{bmatrix}$$ and $$B=\begin{bmatrix}-1&-2&-1\\6&12&6\\5&10&5\end{bmatrix}$$, then which of the following is/are correct?
A and B commute.
AB is null matrix.
Select the correct answer using the code given below :
  • 1 only
  • 2 only
  • Both 1 and 2
  • Neither 1 nor 2
If $$\begin{pmatrix} 2 & 3 \\ 4 & 1 \end{pmatrix}\times \begin{pmatrix} 5 & -2 \\ -3 & 1 \end{pmatrix}=\begin{pmatrix} 1 & -1 \\ 17 & \lambda  \end{pmatrix}$$ then what is $$\lambda $$ equal to?
  • $$7$$
  • $$-7$$
  • $$9$$
  • $$-9$$
If $$\quad A=\begin{pmatrix} 1 & 3 \\ 4 & 5 \end{pmatrix}$$ then $${ A }^{ -1 }$$ equals
  • $$\cfrac { 1 }{ 7 } \left( A+6I \right) $$
  • $$\cfrac { 1 }{ 7 } \left( A-6I \right) $$
  • $$\cfrac { 1 }{ 7 } \left( 6I-A \right) $$
  • None of these
If $$[1\,x\,1]  \begin{bmatrix} 1&3&2 \\ 0&5&1\\0&2&0 \end{bmatrix}$$ $$\begin{bmatrix} 1 \\ 1 \\ x \end{bmatrix}=0$$, then the values of $$x$$ are:
  • $$1,5$$
  • $$-1,-5$$
  • $$1,6$$
  • $$-1,-6$$
  • $$3,3$$
If $$A = \begin{bmatrix} 2& 3\\ -1 & 2\end{bmatrix}$$, then $$A^{3} + 3A^{2} - 4A + 1$$ is equal to
  • $$\begin{bmatrix} 1& 1\\ 1 & 0\end{bmatrix}$$
  • $$\begin{bmatrix} -14& 51\\ -17 & -14\end{bmatrix}$$
  • $$\begin{bmatrix} -14& -51\\ -17 & -14\end{bmatrix}$$
  • $$\begin{bmatrix} -1& -1\\ -1 & 0\end{bmatrix}$$
If $$A=\begin{pmatrix} 3 & 1 \\ -9 & -3 \end{pmatrix}$$ then $${ \left( 1+2A+3{ A }^{ 2 }+....\infty  \right)  }^{ -1 }$$ equals
  • $$\begin{pmatrix} -5 & -2 \\ 18 & 7 \end{pmatrix}$$
  • $$\begin{pmatrix} -5 & 18 \\ -2 & 7 \end{pmatrix}$$
  • $$\begin{pmatrix} 7 & -2 \\ 18 & -5 \end{pmatrix}$$
  • None of these
If $$\begin{bmatrix} \alpha  & \beta  \\ \gamma  & -\alpha  \end{bmatrix}$$ to the square is two rowed unit matrix, then $$\alpha ,\beta ,\gamma $$ should satisfy the relation
  • $$1+{ \alpha }^{ 2 }+\beta \gamma =0$$
  • $$1-{ \alpha }^{ 2 }-\beta \gamma =0$$
  • $$1-{ \alpha }^{ 2 }+\beta \gamma =0$$
  • $${ \alpha }^{ 2 }+\beta \gamma -1=0$$
If $$A=\begin{bmatrix} \alpha  & 0 \\ 1 & 1 \end{bmatrix}$$ and $$B=\begin{bmatrix} 1 & 0 \\ 5 & 1 \end{bmatrix}$$, then value of $$\alpha$$ for which $${A}^{2}=B$$, is
  • $$1$$
  • $$-1$$
  • $$4$$
  • No real value
If $$A = \begin{bmatrix}1 &3 \\ 3 & 4\end{bmatrix}$$ and $$A^{2} - kA - 5I_{2} = 0$$, then the value of $$k$$ is
  • $$3$$
  • $$5$$
  • $$7$$
  • $$-7$$
If $$A=\begin{bmatrix} 1 & -3 \\ 2 & k \end{bmatrix}$$ and $${ A }^{ 2 }-4A+10I=A$$, then $$k$$ is equal to
  • $$0$$
  • $$-4$$
  • $$4$$ and not $$1$$
  • $$1$$ or $$4$$
If $$A = \begin{vmatrix} 5 & x-2 \\ 2x+3 & x+1 \end{vmatrix}$$ is symmetric, then $$x = $$_____
  • $$4$$
  • $$5$$
  • $$-5$$
  • $$-4$$
If $$A$$ is a non zero square matrix of order $$n$$ with $$det\left( I+A \right) \neq 0$$, and $${A}^{3}=0$$, where $$I,O$$ are unit and null matrices of order $$n\times n$$ respectively, then $${ \left( I+A \right)  }^{ -1 }=$$
  • $$I-A+{ A }^{ 2 }$$
  • $$I+A+{ A }^{ 2 }$$
  • $$I+{ A }^{ 2 }$$
  • $$I+A$$
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