hkus10 Posted February 9, 2011 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!
DrRocket Posted February 9, 2011 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
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