Question

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Solve : $\begin{pmatrix}11\:&\:3\:\\ 7\:&\:11\end{pmatrix}\begin{pmatrix}8\:&\:0\:&\:1\:\\ 0\:&\:3\:&\:5\end{pmatrix}$

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Answer 1

Question :

☯ Solve $\begin{pmatrix}11\:&\:3\:\\ 7\:&\:11\end{pmatrix}\begin{pmatrix}8\:&\:0\:&\:1\:\\ 0\:&\:3\:&\:5\end{pmatrix}$

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☞ Your Answer is  $\large \bf{\begin{pmatrix}88&9&26\\ 56&33&62\end{pmatrix}}$

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✭ To Solve : $\begin{pmatrix}11\:&\:3\:\\ 7\:&\:11\end{pmatrix}\begin{pmatrix}8\:&\:0\:&\:1\:\\ 0\:&\:3\:&\:5\end{pmatrix}$

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Given :

✭ First Matrix : $\begin{pmatrix}11\:&\:3\:\\ 7\:&\:11\end{pmatrix}$

✭ Second Matrix : $\begin{pmatrix}8\:&\:0\:&\:1\:\\ 0\:&\:3\:&\:5\end{pmatrix}$

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Solution :

$\\ \longrightarrow\bf{Step\:\:1\:\::Multiply\:the\:rows\:of\:the\:first\:matrix\:by\:the\:columns\:of\:the\:second}\\ {matrix}$

$\begin{pmatrix}11&3\end{pmatrix}\begin{pmatrix}8\\ 0\end{pmatrix}=11\cdot \:8+3\cdot \:0$

$\begin{pmatrix}11&3\end{pmatrix}\begin{pmatrix}0\\ 3\end{pmatrix}=11\cdot \:0+3\cdot \:3$

$\begin{pmatrix}11&3\end{pmatrix}\begin{pmatrix}1\\ 5\end{pmatrix}=11\cdot \:1+3\cdot \:5$

$\begin{pmatrix}7&11\end{pmatrix}\begin{pmatrix}8\\ 0\end{pmatrix}=7\cdot \:8+11\cdot \:0$

$\begin{pmatrix}7&11\end{pmatrix}\begin{pmatrix}0\\ 3\end{pmatrix}=7\cdot \:0+11\cdot \:3$

$\begin{pmatrix}7&11\end{pmatrix}\begin{pmatrix}1\\ 5\end{pmatrix}=7\cdot \:1+11\cdot \:5$

$\large \bf{=\begin{pmatrix}11\cdot \:8+3\cdot \:0&11\cdot \:0+3\cdot \:3&11\cdot \:1+3\cdot \:5\\ 7\cdot \:8+11\cdot \:0&7\cdot \:0+11\cdot \:3&7\cdot \:1+11\cdot \:5\end{pmatrix}}$

$\\ \longrightarrow\bf{Step\:\:2\:\::Simplify\:each\:element}}$

$\large \bf{=\begin{pmatrix}88&9&26\\ 56&33&62\end{pmatrix}}$