M L Aggarwal Solutions for Chapter: Matrices, Exercise 2: EXERCISE 3.2

If $2\left[\begin{array}{cc}1& 3\\ 0& x\end{array}\right]+\left[\begin{array}{cc}y& 0\\ 1& 2\end{array}\right]=\left[\begin{array}{cc}5& 6\\ 1& 8\end{array}\right]$, find the value of $x$ and $y$.

Find $X$ if $Y=\left[\begin{array}{cc}3& 2\\ 1& 4\end{array}\right]$ and $2X+Y=\left[\begin{array}{cc}1& 0\\ -3& 2\end{array}\right]$.

Find matrices $X$ and $Y$ if $X+Y=\left[\begin{array}{cc}7& 0\\ 2& 5\end{array}\right]$ and $X-Y=\left[\begin{array}{cc}3& 0\\ 0& 3\end{array}\right]$.

Find the matrices $X$ and $Y$ if $2X-Y=\left[\begin{array}{ccc}6& -6& 0\\ -4& 2& 1\end{array}\right]$ and $X+2Y=\left[\begin{array}{ccc}3& 2& 5\\ -2& 1& -7\end{array}\right]$.

If $\mathrm{A}=\left[\begin{array}{cc}1& 3\\ 2& 1\\ 3& -1\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{cc}2& 1\\ 1& 2\\ -1& 0\end{array}\right]$, find the matrix $\mathrm{C}$ such that $\mathrm{A}+\mathrm{B}+\mathrm{C}$ is a zero matrix.

Find a matrix $X$ such that $3\mathrm{A}-2\mathrm{B}+X=\mathrm{O}$, where $\mathrm{A}=\left[\begin{array}{cc}4& 2\\ 1& 3\end{array}\right], \mathrm{B}=\left[\begin{array}{cc}-2& 1\\ 3& 2\end{array}\right]$.

If $A=\left[\begin{array}{ll}1& 5\\ 7& 12\end{array}\right]$ and $B=\left[\begin{array}{ll}9& 1\\ 7& 8\end{array}\right]$, find a matrix $C$ such that $3A+5B+2C$ is a null matrix.

If $\mathrm{A}=\left[\begin{array}{cc}8& 0\\ 4& -2\\ 3& 6\end{array}\right]$ and $\mathrm{B}=\left[\begin{array}{cc}2& -2\\ 4& 2\\ -5& 1\end{array}\right]$, then find matrix $X$ such that $2\mathrm{A}+3X=5\mathrm{B}$.