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Question
If P=⎡⎢⎣12−33−12−213⎤⎥⎦, Q=⎡⎢⎣231312123⎤⎥⎦, then find matrix R such that P+Q+R is a zero matrix.
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Solution
Here, P+Q+R=OSo, R=O−P−QR=⎡⎢⎣000000000⎤⎥⎦−⎡⎢⎣12−33−12−213⎤⎥⎦−⎡⎢⎣231312123⎤⎥⎦R=⎡⎢⎣000000000⎤⎥⎦+⎡⎢⎣−1−23−31−22−1−3⎤⎥⎦+⎡⎢⎣−2−3−1−3−1−2−1−2−3⎤⎥⎦R=⎡⎢⎣0−1−20−2−30+3−10−3−30+1−10−2−20+2−10−1−20−3−3⎤⎥⎦R=⎡⎢⎣−3−52−60−41−3−6⎤⎥⎦
So, R=O−P−Q
R=⎡⎢⎣000000000⎤⎥⎦−⎡⎢⎣12−33−12−213⎤⎥⎦−⎡⎢⎣231312123⎤⎥⎦R=⎡⎢⎣000000000⎤⎥⎦+⎡⎢⎣−1−23−31−22−1−3⎤⎥⎦+⎡⎢⎣−2−3−1−3−1−2−1−2−3⎤⎥⎦R=⎡⎢⎣0−1−20−2−30+3−10−3−30+1−10−2−20+2−10−1−20−3−3⎤⎥⎦R=⎡⎢⎣−3−52−60−41−3−6⎤⎥⎦
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