13. Prove the following: Let A be an m x n matrix, X be an n x...

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13. Prove the following: Let A be an m x n matrix, X be an n x r matrix, C be an m x r matrix, B be an r x g matrix, and D be an n x g matrix. A necessary and sufficient condition that the two equations AX = C and XB = D have a common solution X is (1) each equation has a solution and (2) AD = CB.

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