Let $A = \begin{bmatrix} 2+i & 4 \\ 1+i & 2+4i \end{bmatrix}$, $B = \begin{bmatrix} -i & 4 \\ 2+2i & 1+4i \end{bmatrix}$, $C = \begin{bmatrix} 0 & 4+i \\ -3i & 1+i \end{bmatrix}$. Find each linear combination. (a) $C - (1+i)A$ (b) $iA - (1-i)B - 4C$
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Step 1
First, let's compute $(1+i)A$: $(1+i)A = (1+i)\begin{bmatrix} 2+i & 4 \\ 1+i & 2+4i \end{bmatrix} = \begin{bmatrix} (1+i)(2+i) & 4(1+i) \\ (1+i)(1+i) & (1+i)(2+4i) \end{bmatrix} = \begin{bmatrix} 2+i+2i+i^2 & 4+4i \\ 1+2i+i^2 & 2+4i+2i+4i^2 \end{bmatrix} = Show more…
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