Solving Ax=b | Linear Algebra | Mathematics | MIT OpenCourseWare
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SOLVED: Suppose A, B, and X are nxn matrices with A, X, and A - AX invertible, and suppose that (A-AX) = X B. Complete parts (a) and (b) below:Explain why B is invertible. Choose the correct answer below:Multiply both sides of the equation (A - AX)^-1 = X^" B by B^-1 to obtain X^-1 = (A - AX)^-1 B^-1. Now multiply both sides by (A - AX) to obtain the equation B = (A - AX)X^-1. Thus, the inverse of B exists and B must be invertible.Solving the equation (A - AX)^-1 = X^-1 B for B yields X(A - AX)^
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