Properties of Orthogonal Matrix

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"Ans. (A)From theproperty of orthogonalmatrix ,T ?1 As, ??BB ? ?? Consider the given equation from L.H.S. and expand it,T?? 11 T T T T T T T (AB) ?B A ?B A ?B A ?B A ?B A ?B (A ?A) ? 0Now,If B is orthogonal then it cannot be zero,So,T (AA ?? ) 0 T AA..

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"Ans. (A)From theproperty of orthogonalmatrix ,T ?1 As, ??BB ? ?? Consider the given equation from L.H.S. and expand it,T?? 11 T T T T T T T (AB) ?B A ?B A ?B A ?B A ?B A ?B (A ?A) ? 0Now,If B is orthogonal then it cannot be zero,So,T (AA ?? ) 0 T AA ?? So, A is ant symmetric,(B)Again, from the above given equation,?1 T B A ??() AB TT A ??BB A Now, Take determinant on both side,3 2 2 det(A) ? ( ?1) det(A)det(B) ? ?det(A)det(B) Take, the term det(A) common,2 (1?? det(BA ) )det( ) 0From the above equation, det(A) ? 0? ? So, A is singular. "

Unit 2 Project - Quadratic Function

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