EM-2130

Matrix multiplication

E Math · Secondary 4 · Hard · Matrix multiplication

A company produces two types of gadgets, A and B. The weekly production is represented by matrix

P = \begin{pmatrix} 4 & 2 & 3 \\1 & 5 & 2 \end{pmatrix}

, where the columns are Factory 1, Factory 2 and Factory 3.
Each gadget A costs \$6 to make and each gadget B costs \$9 to make.
Represent the costs in a suitable column matrix

S

, then find the matrix

C = P^TS

$C = \begin{pmatrix}33\\57\\36\end{pmatrix}$
$C = \begin{pmatrix}36\\51\\42\end{pmatrix}$
$C = \begin{pmatrix}24 & 12 & 18\\6 & 30 & 12\end{pmatrix}$
$C = \begin{pmatrix}78\\51\\36\end{pmatrix}$

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