Let

Question:

Let $A=\left[\begin{array}{rrr}-1 & 0 & 2 \\ 3 & 1 & 4\end{array}\right], B=\left[\begin{array}{lll}0 & -2 & 5 \\ 1 & -3 & 1\end{array}\right]$ and $C=\left[\begin{array}{rrr}1 & -5 & 2 \\ 6 & 0 & -4\end{array}\right]$. Compute $2 A-3 B+4 C$.

Solution:

Here,

$2 A-3 B+4 C=2\left[\begin{array}{ccc}-1 & 0 & 2 \\ 3 & 1 & 4\end{array}\right]-3\left[\begin{array}{ccc}0 & -2 & 5 \\ 1 & -3 & 1\end{array}\right]+4\left[\begin{array}{ccc}1 & -5 & 2 \\ 6 & 0 & -4\end{array}\right]$

$\Rightarrow 2 A-3 B+4 C=\left[\begin{array}{ccc}-2 & 0 & 4 \\ 6 & 2 & 8\end{array}\right]-\left[\begin{array}{ccc}0 & -6 & 15 \\ 3 & -9 & 3\end{array}\right]+\left[\begin{array}{ccc}4 & -20 & 8 \\ 24 & 0 & -16\end{array}\right]$

$\Rightarrow 2 A-3 B+4 C=\left[\begin{array}{ccc}-2-0+4 & 0+6-20 & 4-15+8 \\ 6-3+24 & 2+9+0 & 8-3-16\end{array}\right]$

$\Rightarrow 2 A-3 B+4 C=\left[\begin{array}{ccc}2 & -14 & -3 \\ 27 & 11 & -11\end{array}\right]$

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