Answer
No, this $\vec{b}$ is not in the range of this linear transformation.
Work Step by Step
We row reduce the augmented matrix $[\mathbf{A}\ \vec{b}]$ and find that, in producing an echelon matrix, we have a row of the form $[0\ 0\ 0\ 0\ 1]$. Hence, by Theorem 2, the equation is inconsistent.
