I cannot use the matrix inverse theorem, yet I have to show this, thanks in advance.

If the equation Ax = b has at least one solution for each b in Rn, then the equationAx= 0 has only the trivial solution.

thanks in advance

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- Mar 19th 2013, 04:49 PMTrystanandEmma1I have to show this proof for the matrix inverse theorem
I cannot use the matrix inverse theorem, yet I have to show this, thanks in advance.

If the equation Ax = b has at least one solution for each b in Rn, then the equation*Ax*= 0 has only the trivial solution.

thanks in advance - Mar 19th 2013, 04:52 PMProve ItRe: I have to show this proof for the matrix inverse theorem
Isn't it because the only matrix you could multiply x by to get the a zero vector is the zero matrix, and that the determinant of the zero matrix is 0?