Solution
= Solution
\b[False.] Take $A=(1,0)^T$, an $m=2$, $n=1$ <matrix> of <matrix rank> one, and $b=(0,1)^T$. Then $Ax=(x,0)^T$ never equals $b$. <Full column rank> implies injectivity, not surjectivity onto a larger codomain.
= Solution
\b[False.] Take $A=(1,0)^T$, an $m=2$, $n=1$ <matrix> of <matrix rank> one, and $b=(0,1)^T$. Then $Ax=(x,0)^T$ never equals $b$. <Full column rank> implies injectivity, not surjectivity onto a larger codomain.