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Question
Let A = `[[-1 0 2],[3 1 4]]``B=[[0 -2 5],[1 -3 1]]``and C = [[1 -5 2],[6 0 -4 ]]`Compute2A2-3B +4C :
Solution
\[Here, \]
\[2A - 3B + 4C = 2\begin{bmatrix}- 1 & 0 & 2 \\ 3 & 1 & 4\end{bmatrix} - 3\begin{bmatrix}0 & - 2 & 5 \\ 1 & - 3 & 1\end{bmatrix} + 4\begin{bmatrix}1 & - 5 & 2 \\ 6 & 0 & - 4\end{bmatrix}\]
\[ \Rightarrow 2A - 3B + 4C = \begin{bmatrix}- 2 & 0 & 4 \\ 6 & 2 & 8\end{bmatrix} - \begin{bmatrix}0 & - 6 & 15 \\ 3 & - 9 & 3\end{bmatrix} + \begin{bmatrix}4 & - 20 & 8 \\ 24 & 0 & - 16\end{bmatrix}\]
\[ \Rightarrow 2A - 3B + 4C = \begin{bmatrix}- 2 - 0 + 4 & 0 + 6 - 20 & 4 - 15 + 8 \\ 6 - 3 + 24 & 2 + 9 + 0 & 8 - 3 - 16\end{bmatrix}\]
\[ \Rightarrow 2A - 3B + 4C = \begin{bmatrix}2 & - 14 & - 3 \\ 27 & 11 & - 11\end{bmatrix}\]
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