Matrices digital book with solutions

Q. 1/89· Easy

If $A=\left[ \begin{array}{ll}1 & 2 \\ 3 & 4\end{array} \right]$ then $A^{-1}$ =

Q. 2/89· Easy

If $A=\left[ \begin{array}{ll}1 & 1 \\ 1 & 1\end{array} \right]$ then $A^{100}$ :

Q. 3/89· Easy

If $A=\left[\begin{array}{ccc}3 & 0 & 0 \\ 0 & -5 & 0 \\ 0 & 0 & 7\end{array}\right] ; B=\left[\begin{array}{ccc}-1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{array}\right]$ then, $(2 A+3 B)^{-1}=$ $\_\_\_\_$

Q. 4/89· Easy

Inverse of the matrix $\left[\begin{array}{cc}0.8 & -0.6 \\ 0.6 & 0.8\end{array}\right]$ is

Q. 5/89· Easy

If $A=\left[ \begin{array}{lll}1 & 1 & 0 \\ 2 & 1 & 5 \\ 1 & 2 & 1\end{array} \right]$ , then $a_{11}A_{21}+a_{12}A_{22}+a_{13}A_{23}$ is equal to (where $A_{ij}$ stand for cofactor)

Q. 6/89· Easy

If matrix $A=\left[ \begin{array}{ll}1 & 2 \\ 4 & 3\end{array} \right]$ , such that $AX=I$ , then $X$ is equal to

Q. 7/89· Easy

If $A=\left[ \begin{array}{ll}1 & 5 \\ 2 & 7\end{array} \right]$ then $A^{-1}$ =

Q. 8/89· Easy

If $A=\left[ \begin{array}{ccc}1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0\end{array} \right]$ and $A(adjA)=KI$ , then the value of $K$ is (where $I$ is unit matrix of order 3)

Q. 9/89· Easy

If $A=\left[ \begin{array}{cc}2 & -1 \\ -1 & 2\end{array} \right]$ such that $A^{2}-4A+3I=0$ where $I$ is a unit matrix of order, 2 , then $A^{-1}$ is

Q. 10/89· Easy

If $A=\left[ \begin{array}{ccc}0 & -4 & 1 \\ 2 & \lambda & -3 \\ 1 & 2 & -1\end{array} \right]$ , then $A^{-1}$ exists (i.e., $A$ is invertible) if

Q. 11/89· Easy

If matrix $A=\left[ \begin{array}{ccc}3 & -2 & 4 \\ 1 & 2 & -1 \\ 0 & 1 & 1\end{array} \right]$ and $A^{-1}=\dfrac{1}{k}adj(A)$ , then $k$ is

Q. 12/89· Easy

If $A=\left[ \begin{array}{ll}2 & 1 \\ 0 & x\end{array} \right]$ and $A^{-1}=\left[ \begin{array}{ll}\dfrac{1}{2} & \dfrac{1}{6} \\ 0 & \dfrac{1}{x}\end{array} \right]$ , then the value of $x$ is equal to

Q. 13/89· Easy

If $A$ is 3 $\times$ 2 matrix and $B$ is a matrix such that $A^{'}B$ and $BA^{'}$ are both defined. Then, order of matrix $B$ is-

Q. 14/89· Easy

Inverse of $\left[\begin{array}{cc}3 & -2 \\ 1 & 4\end{array}\right]$ is

Q. 15/89· Easy

If $A=\left[\begin{array}{cc}1 & -5 \\ -2 & 4\end{array}\right]$ , then $A^{-1}=$