Let V = Rx be the vector space of all real 2 2 matrices with real...

 

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Let V = Rx be the vector space of all real 2 2 matrices with real inner product given < A, B >= tr(BTA), where tr is the trace of a matrix (i.e., sum of the main diagonal entries of the matrix). Let 03 14 A B 32 02 (a) Find < A, B > and ||B||, where ||-|| denotes the norm(length) induced by the given inner product. (b) Are A and B orthogonal?(:) (c) Determine the scalar c such that A-cB is orthogonal to A. Let V = Rx be the vector space of all real 2 2 matrices with real inner product given < A, B >= tr(BTA), where tr is the trace of a matrix (i.e., sum of the main diagonal entries of the matrix). Let 03 14 A B 32 02 (a) Find < A, B > and ||B||, where ||-|| denotes the norm(length) induced by the given inner product. (b) Are A and B orthogonal?(:) (c) Determine the scalar c such that A-cB is orthogonal to A.