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Question
If A = `([cos alpha, sin alpha],[-sinalpha, cos alpha])` , find α satisfying 0 < α < `pi/r`when `A+A^T=sqrt2I_2` where AT is transpose of A.
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Solution
Consider the given matrix
A = `[(cosalpha, sin alpha),(-sinalpha,cos alpha)]0<alpha<pi/2`
`A+A^T=sqrt2I_2`
`[(cosalpha, sin alpha),(-sinalpha, cos alpha)]+[(cosalpha,-sinalpha),(sinalpha,cos alpha)]=sqrt2[(1,0),(0,1)]`
`[(2cosalpha, 0),(0,2cosalpha)]=[(sqrt2,0),(0, sqrt2)]`
`2cosalpha=sqrt2`
`cosalpha=sqrt2/2=1/sqrt2`
`alpha=pi/4`
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