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If A = \(\begin{bmatrix}x&y\\[0.3em]z&w\end{bmatrix},\) B = \(\begin{bmatrix}x&-y\\[0.3em]-z&w\end{bmatrix}\) and C = \(\begin{bmatrix}-2x&0\\[0.3em]0&-2w\end{bmatrix},\) then A + B + C is a

(a) identity matrix 

(b) null matrix 

(c) row matrix 

(d) column matrix

1 Answer

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Best answer

(b) A + B + C = \(\begin{bmatrix}x&y\\[0.3em]z&w\end{bmatrix}\)\(\begin{bmatrix}x&-y\\[0.3em]-z&w\end{bmatrix}\)\(\begin{bmatrix}-2x&0\\[0.3em]0&-2w\end{bmatrix}\)

\(\begin{bmatrix}x+x+(-2y)&y+(-y)+0\\[0.3em]z+(-z)+0&w+w+(-2w)\end{bmatrix}\)

\(\begin{bmatrix}0&0\\[0.3em]0&0\end{bmatrix}\)

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