In my text there is a T/F statement: If every row of an $m \times n$ matrix A contains a pivot position, then the matrix equation $Ax=b$ is consistent for every b in $R^n$
This is listed as true.
I thought about a $2 \times 3$ matrix...
Doesn't this require that since $b$ will be a $2\times1$ matrix, $Ax=b$ would be consistent for every b in $R^m$ ($R^2$ in my example)?
For it to span $R^n$ wouldn't it be required that the columns of A span $R^3$ in my example (impossible)?