InterviewSolution
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InterviewSolution
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If A=[{:(cos alpha,sin alpha),(-sin alpha, cos alpha):}] and A^(-1)=A' then find the value of alpha. |
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Answer» SOLUTION :We have, `A=[{:(cos a,sina),(-SIN a,cosa):}]` and `A'=[{:(cos a,-sina),(sina,cosa):}]` Also, `A^(-1)=A`' `rArr A A^(-1)=A A`' `rArr I=[{:(cos alpha,sin alpha),(-sin alpha,cos alpha):}]` `rArr [{:(1,0),(0,1):}]=[{:(cos^(2)alpha+sin^(2)alpha, 0),(0,sin^(2)alpha+cos^(2)alpha):}]` By using EQUALITY of matrices, we get `cos^(2)alpha+sin^(2)alpha=1` which is true for all REAL values of `alpha`. |
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