If . Find 2PQ.

Engineering

Mathematics

Algebra of Matrices

Multiplication of Matrices

Question

If $P = [\begin{array}{cc} 4 & 6 \\ 2 & - 8 \end{array}], Q = [\begin{array}{cc} 2 & - 3 \\ - 1 & 1 \end{array}]$ . Find 2PQ.

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Given
$P = [\begin{array}{cc} 4 & 6 \\ 2 & - 8 \end{array}]$

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

$2 PQ = 2 [\begin{array}{rr} 4 & 6 \\ 2 & - 8 \end{array}] \times [\begin{array}{rr} 2 & - 3 \\ - 1 & 1 \end{array}]$

$= 2 [\begin{array}{cc} 8 - 6 & - 12 + 6 \\ 4 + 8 & - 6 - 8 \end{array}] = 2 [\begin{array}{cc} 8 & - 6 \\ 12 & - 14 \end{array}] = [\begin{array}{cc} 4 & - 12 \\ 24 & - 28 \end{array}]$