If and , then find 2X

Engineering

Mathematics

Algebra of Matrices

Question

If $X = [\begin{array}{ccc} 3 & 1 & - 1 \\ 5 & - 2 & - 3 \end{array}]$ and $Y = [\begin{array}{ccc} 2 & 1 & - 1 \\ 7 & 2 & 4 \end{array}]$ , then find 2X – 3Y.

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We have, $X = {[\begin{array}{ccc} 3 & 1 & - 1 \\ 5 & - 2 & - 3 \end{array}]}_{2 \times 3}$ and $Y = {[\begin{array}{ccc} 2 & 1 & - 1 \\ 7 & 2 & 4 \end{array}]}_{2 \times 3}$
$∵ 2 x = 2 [\begin{array}{ccc} 3 & 1 & - 1 \\ 5 & - 2 & - 3 \end{array}] = [\begin{array}{ccc} 6 & 2 & - 2 \\ 10 & - 4 & - 6 \end{array}]$
and $3 y = 3 [\begin{array}{ccc} 2 & 1 & - 1 \\ 7 & 2 & 4 \end{array}] = [\begin{array}{ccc} 6 & 3 & - 3 \\ 21 & 6 & 12 \end{array}]$
$∴ 2 x - 3 y = [\begin{array}{ccc} 6 - 6 & 2 - 3 & - 2 + 3 \\ 10 - 21 & - 4 - 6 & - 6 - 12 \end{array}] = [\begin{array}{ccc} 0 & - 1 & 1 \\ - 11 & - 10 & - 18 \end{array}]$