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If A=[[cosalpha,-sinalpha],[sinalpha,cos...

If `A=[[cosalpha,-sinalpha],[sinalpha,cosalpha]]`, then `A+A^(prime)=I`, if the value of `alpha`is (A) `pi/6` (b) `pi/3` (c) `pi` (d) `(3pi)/2`

Text Solution

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`A = [[cos alpha, -sinalpha],[sinalpha, cos alpha]]`
`:. A^T = [[cosalpha, sin alpha],[-sin alpha, cos alpha]]`

We are given, `A + A^T = I`
`:. [[cos alpha, -sinalpha],[sinalpha, cos alpha]]+[[cosalpha, sin alpha],[-sin alpha, cos alpha]] = [[1,0],[0,1]]`
`=>[[2cosalpha,0],[0,2cosalpha]] = [[1,0],[0,1]]`
`:. 2cos alpha = 1`
`=> cos alpha = 1/2`
`=>alpha = pi/3`
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