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If $X=\left[ \begin{matrix} 17 & 5 & 19 \\ 11 & 8 & 13 \\ \end{matrix} \right]$and $Y=\left[ \begin{matrix} 9 & 3 & 7 \\ 1 & 6 & 5 \\ \end{matrix} \right]$ . Find $2X-3Y$

Given, two X and Y matrices are rectangular matrices of $2\times 3$.

Then,

$2X=\left[ \begin{matrix}

17\times 2 & 5\times 2 & 19\times 2  \\

11\times 2 & 8\times 2 & 13\times 2  \\

\end{matrix} \right]$

$=\left[ \begin{matrix}

34 & 10 & 38  \\

22 & 16 & 26  \\

\end{matrix} \right]$

$3Y=\left[ \begin{matrix}

9\times 3 & 3\times 3 & 7\times 3  \\

1\times 3 & 6\times 3 & 5\times 3  \\

\end{matrix} \right]$

$=\left[ \begin{matrix}

27 & 9 & 21  \\

3 & 18 & 15  \\

\end{matrix} \right]$

Then,

$2X-3Y=\left[ \begin{matrix}

34-27 & 10-9 & 38-21  \\

22-3 & 16-18 & 26-15  \\

\end{matrix} \right]$

$=\left[ \begin{matrix}

7 & 1 & 17  \\

19 & -2 & 11  \\

\end{matrix} \right]$