I have a question here:
Suppose A is a 5x6 matrix and all solutions of Ax = 0 are multiples of one nonzero vector. Will the equation Ax = b be solvable for all b?
I'm not sure where to go with this question. I have a theorem here that says: The column space of an m x n matrix A, is all of \(\displaystyle \mathbb{R}^m\) if and only if Ax = b has a solution for all b E \(\displaystyle \mathbb{R}^m\)
Could someone give me a hint/direction?
Suppose A is a 5x6 matrix and all solutions of Ax = 0 are multiples of one nonzero vector. Will the equation Ax = b be solvable for all b?
I'm not sure where to go with this question. I have a theorem here that says: The column space of an m x n matrix A, is all of \(\displaystyle \mathbb{R}^m\) if and only if Ax = b has a solution for all b E \(\displaystyle \mathbb{R}^m\)
Could someone give me a hint/direction?