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Linear Equation and Matrices

hkus10
in Homework Help

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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!

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.

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