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Question 3.1.14: Calculate [2 3 4 1][5 1 -2 7].

Calculate \left [ \begin{matrix} 2 & 3 \\ 4 & 1 \end{matrix} \right ] \left [ \begin{matrix} 5 & 1 \\ -2 & 7 \end{matrix} \right ].

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Taking dot products of the rows of the first matrix with columns of the second matrix gives

\left [ \begin{matrix} 2 & 3 \\ 4 & 1 \end{matrix} \right ] \left [ \begin{matrix} 5 & 1 \\ -2 & 7 \end{matrix} \right ] = \left [ \begin{matrix} 2(5) + 3(−2) & 2(1) + 3(7) \\ 4(5) + 1(−2) & 4(1) + 1(7) \end{matrix} \right ] = \left [ \begin{matrix} 4 & 23 \\ 18 & 11 \end{matrix} \right ]

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