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Question

# Perform the indicated matrix operations. If the matrix does not exist, write impossible.$4\left[\begin{array}{rrrrr}1 & 0 & -2 & 3 & 1 \\ -4 & 5 & 2 & -1 & 0\end{array}\right]$

Solution

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Step 1
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Multiply every terms in the matrix by $4$:

\begin{aligned} 4\cdot\begin{bmatrix} 1 & 0 & -2 & 3 & 1 \\ -4 & 5 & 2 & -1 & 0 \\ \end{bmatrix}&= \begin{bmatrix} 4\cdot 1 & 4\cdot0 & 4\cdot(-2) & 4\cdot3 & 4\cdot1 \\ 4\cdot (-4) & 4\cdot5 & 4\cdot2 & 4\cdot(-1) & 4\cdot0 \\ \end{bmatrix}\\ &=\begin{bmatrix} 4 & 0 & -8 & 12 & 4 \\ -16 & 20 & 8 & -4 & 0 \\ \end{bmatrix} \end{aligned}

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