EM-2090

Matrix multiplication

E Math · Secondary 4 · Hard · Matrix multiplication

A shop mixes three juices: Apple (A), Berry (B) and Citrus (C). One bottle of Mix X uses 1 L of A, 2 L of B and 1 L of C. One bottle of Mix Y uses 2 L of A, 1 L of B and 3 L of C. One bottle of Mix Z uses 1 L of A, 1 L of B and 2 L of C. The matrix of requirements is

M = \begin{pmatrix}1 & 2 & 1\\2 & 1 & 1\\1 & 3 & 2\end{pmatrix}

where columns represent X, Y, Z and rows represent A, B, C.
The shop plans to make 3 bottles of X, 4 bottles of Y and

k

bottles of Z. Represent this as a column matrix

N

and find

MN

in terms of

k

$MN = \begin{pmatrix}11 + k\\10 + k\\15 + 2k\end{pmatrix}$
$MN = \begin{pmatrix}11 + 2k\\10 + k\\15 + 2k\end{pmatrix}$
$MN = \begin{pmatrix}7 + k\\10 + 2k\\15 + 2k\end{pmatrix}$
$MN = \begin{pmatrix}11 + k\\10 + 2k\\15 + k\end{pmatrix}$

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