hkus10 Posted January 30, 2011 Share Posted January 30, 2011 1) show that if AB = AC and A is nonsingular, then B = C. 2) show that if A is nonsingular and AB = 0 for an n x n matrix B, then B = 0. 3) Consider the homogenous system Ax=0, where A is n x n. If A is nonsingular, show that the only solution is the trivial one, x=0. 4) Prove that if A is symmetric and nonsingular, then A^-1 is symmetric. Please help and show all your work or at least give me some directions! Thanks Link to comment Share on other sites More sharing options...
DrRocket Posted February 11, 2011 Share Posted February 11, 2011 1) show that if AB = AC and A is nonsingular, then B = C. 2) show that if A is nonsingular and AB = 0 for an n x n matrix B, then B = 0. 3) Consider the homogenous system Ax=0, where A is n x n. If A is nonsingular, show that the only solution is the trivial one, x=0. 4) Prove that if A is symmetric and nonsingular, then A^-1 is symmetric. Please help and show all your work or at least give me some directions! Thanks Hint. None of these should take more than about five steps, and most quite a bit fewer. Link to comment Share on other sites More sharing options...
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