Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Digital systems, linear algebra, introduction to formal proof resit / 5 / a / ii

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.