LA2.1.1

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If $A=\begin{bmatrix} 0 & 1 & 2 \\ 2 & 3 & 4 \end{bmatrix}\,$ and $B=\begin{bmatrix} 1 & 0 & 0 \\ 2 & -3 & 1 \end{bmatrix}\,$ evaluate $2A+3B\,$

$2A+3B=2\begin{bmatrix} 0 & 1 & 2 \\ 2 & 3 & 4 \end{bmatrix}+3\begin{bmatrix} 1 & 0 & 0 \\ 2 & -3 & 1 \end{bmatrix}\,$ which is equal to

$\begin{bmatrix} 0 & 2 & 4 \\ 4 & 6 & 8 \end{bmatrix}+\begin{bmatrix} 3 & 0 & 0 \\ 6 & -9 & 3 \end{bmatrix}\,$

$\begin{bmatrix} 0+3 & 2+0 & 4+0 \\ 4+6 & 6-9 & 8+3 \end{bmatrix}=\begin{bmatrix} 3 & 2 & 4 \\ 10 & -3 & 11 \end{bmatrix}\,$

Main Page:Linear Algebra

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