Compute the indicated products

Engineering

Mathematics

Multiplication of Matrices

Question

Compute the indicated products
$[\begin{array}{cc} 1 & - 2 \\ 2 & 3 \end{array}] [\begin{array}{ccc} 1 & 2 & 3 \\ 2 & 3 & 1 \end{array}]$

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$[\begin{array}{cc} 1 & - 2 \\ 2 & 3 \end{array}] [\begin{array}{ccc} 1 & 2 & 3 \\ 2 & 3 & 1 \end{array}]$

= [\begin{array}{ccc} 1 \times 1 + (- 2) \times 2 & 1 \times 2 + (- 2) \times 3 & 1 \times 3 (- 2) \times 1 \\ 2 \times 1 + 3 \times 2 & 2 \times 2 + 3 \times 3 & 2 \times 3 + 3 \times 1 \end{array}]

= {[\begin{array}{ccc} - 3 & - 4 & 1 \\ 8 & 13 & 9 \end{array}]}_{2 \times 3}