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Let A=B B^(T)+C C^(T), where B=[(cos the...

Let `A=B B^(T)+C C^(T)`, where `B=[(cos theta),(sin theta)], C=[(sin theta),(-cos theta)], theta in R`. Then prove that a is unit matrix.

Text Solution

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`A=B B^(T)+C C^(T)`
`=[(cos theta),(sin theta)][(cos theta),(sin theta)]+[(sin theta),(-cos theta)][(sin theta, -cos theta)]`
`=[(cos^(2) theta,cos theta . sin theta),(sin theta.costheta,sin^(2) theta)]+[(sin^(2) theta,0sintheta.cos theta),(-sin theta. cos theta,cos^(2) theta)]`
`=[(1,0),(0,1)]`
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