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Question
If A=diag(2 −5 9),B=diag(1 1 −4) and C=diag(−6 3 4), then find A−2B.
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Solution
Here, A=⎡⎢⎣2000−50009⎤⎥⎦ and B=⎡⎢⎣10001000−4⎤⎥⎦
⇒ A−2B= ⎡⎢⎣2000−50009⎤⎥⎦−2⎡⎢⎣10001000−4⎤⎥⎦
=⎡⎢⎣2000−50009⎤⎥⎦−⎡⎢⎣1×20×20×20×21×20×20×20×2−4×2⎤⎥⎦
=⎡⎢⎣2000−50009⎤⎥⎦−⎡⎢⎣20002000−8⎤⎥⎦
=⎡⎢⎣2−20−00−00−0−5−20−00−00−09−(−8)⎤⎥⎦
=⎡⎢⎣0000−700017⎤⎥⎦=diag(0−717)
⇒ A−2B= ⎡⎢⎣2000−50009⎤⎥⎦−2⎡⎢⎣10001000−4⎤⎥⎦
=⎡⎢⎣2000−50009⎤⎥⎦−⎡⎢⎣1×20×20×20×21×20×20×20×2−4×2⎤⎥⎦
=⎡⎢⎣2000−50009⎤⎥⎦−⎡⎢⎣20002000−8⎤⎥⎦
=⎡⎢⎣2−20−00−00−0−5−20−00−00−09−(−8)⎤⎥⎦
=⎡⎢⎣0000−700017⎤⎥⎦=diag(0−717)
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