Let A, B be (n x n)-matrices. Suppose AB = BA = In.(a) Let X,...
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Let A, B be (n x n)-matrices. Suppose AB = BA = In.(a) Let X, C be n m matrices.Show that AX = C if and only if X = BC.(b) Let b be a column vector of size n.Suppose u is a solution of LS(A, b) (which is the linear system with coefficient matrix A and vector of constant b). Express u in terms of B and b.(c) Let 1 0 1 -5 1 1 3 a= 5 1 3 B= 7 -1 -2 b= 2 1 -1 2 6 -1 -1 1I). Verify that AB = BA= I?.ii). Hence, or otherwise, find a solution of LS(A, b)."=
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