hkus10 Posted February 9, 2011 Share Posted February 9, 2011 1) Let A be an n x n matrix. Prove that if Ax= 0 for all n x 1matrices, then A=O. Can you show me the steps of solving this problem? Please! Link to comment Share on other sites More sharing options...
DrRocket Posted February 9, 2011 Share Posted February 9, 2011 1) Let A be an n x n matrix. Prove that if Ax= 0 for all n x 1matrices, then A=O. Can you show me the steps of solving this problem? Please! If Ax=0 for all vectors x (nx1 matrices) then A represents the 0 linear function and is represented by the 0 matrix for any choice of basis vectors. Or you might consider what happens when you apply A to a basis vector and what that tells you about the matrix representation for A. 1 Link to comment Share on other sites More sharing options...
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