Answer
$b$ is not a linear combination of the column vectors of $A$.
Work Step by Step
The question posed is equivalent to asking whether the system represented by the augmented matrix below is consistent:
$$
\begin{bmatrix}
1 & -4 & 2 & 3 \\
0 & 3 & 5 & -7 \\
-2 & 8 & -4 & -3 \\
\end{bmatrix}
$$
We can do this via row reduction. Begin by adding twice the first row to the third row:
$$
\begin{bmatrix}
1 & -4 & 2 & 3 \\
0 & 3 & 5 & -7 \\
0 & 0 & 0 & 3 \\
\end{bmatrix}
$$
We see the contraction $0=3$; thus, the system is inconsistent and $b$ is not a linear combination of the columns of $A$.
