If A=⎡⎢⎣1010201−14⎤⎥⎦,A=B+C,B=BT,C=−CT, then C is equal to
A
⎡⎢⎣00.50−0.500000⎤⎥⎦
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B
⎡⎢⎣000000.50−0.50⎤⎥⎦
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C
⎡⎢⎣00.50−0.500.50−0.50⎤⎥⎦
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D
⎡⎢⎣0−0.50.50.500.5−0500⎤⎥⎦
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Solution
The correct option is B⎡⎢⎣000000.50−0.50⎤⎥⎦ Given, A=⎡⎢⎣1010201−14⎤⎥⎦ Since A=B+C and B=BT,C=−CT
A can be represented as A=12(A+AT)+12(A−AT)∴12(A+AT)=B and 12(A−AT)=C2C=⎡⎢⎣1010201−14⎤⎥⎦−⎡⎢⎣10102−1104⎤⎥⎦=⎡⎢⎣0000010−10⎤⎥⎦C=⎡⎢⎣000000.50−0.50⎤⎥⎦