T or F
If $\mathbf{A}\vec{x} = \vec{b_{1}}$ has no solution, $\mathbf{A}\vec{x} = \vec{b_{2}}$ has many solutions, then $\mathbf{A}\vec{x} = \vec{b_{1}} + \vec{b_{2}}$ has many solutions.
This is false because the addition of the two $\vec{b}$ vectors doesn't mean the sum is a multiple of either $\vec{b_{1}}$ or $\vec{b_{2}}$ and will not necessarily fall in the same plane as either? Meaning it could result in either no solution or many solutions since $\mathbf A$ doesn't span the whole space?