Question

If $X$ and $Y$ are the matrices of order $2\times 2$ each and $2X-3Y=\left[\begin{array}{cc}-7& 0\\ 7& -13\end{array}\right]$ and $3X+2Y=\left[\begin{array}{cc}9& 13\\ 4& 13\end{array}\right]$, then what is $Y$ equal to?

• A. $\left[\begin{array}{cc}1& 3\\ -2& 1\end{array}\right]$
• B. $\left[\begin{array}{cc}1& 3\\ 2& 1\end{array}\right]$
• C. $\left[\begin{array}{cc}3& 2\\ -1& 5\end{array}\right]$
• D. $\left[\begin{array}{cc}3& 2\\ 1& -5\end{array}\right]$

Answer 1

The correct option is C $\left[\begin{array}{cc}3& 2\\ -1& 5\end{array}\right]$

$3\times (2x-34=\left[\begin{array}{cc}-7& 0\\ 7& -13\end{array}\right])\Rightarrow 6x-9y=\left[\begin{array}{cc}-21& 0\\ 21& -39\end{array}\right]$

$2\times (3x+2y=\left[\begin{array}{cc}9& 13\\ 4& 13\end{array}\right])$ $\Rightarrow 6x+4y=\left[\begin{array}{cc}18& 26\\ 8& 26\end{array}\right]$

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$-13y=\left[\begin{array}{cc}-39& -26\\ 13& -65\end{array}\right]$

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$\therefore y=\left[\begin{array}{cc}3& 2\\ -1& 5\end{array}\right]$.