Matrix Times Vector, Checked Two Ways

$A = \begin{bmatrix} 3 & -2 & 1 \\ 0 & 4 & -1 \\ 2 & 1 & 5 \end{bmatrix}, \qquad v = \begin{bmatrix} 2 \\ -1 \\ 3 \end{bmatrix}$

There are two equivalent ways to read the product $Av$:

• Row view: entry $i$ of the answer is the dot product of row $i$ of $A$ with $v$.
• Column view: the whole answer is $v_1 c_1 + v_2 c_2 + v_3 c_3$, where $c_k$ is column $k$ of $A$ — a weighted blend of $A$'s columns, with the weights taken from $v$ in order.

Both routes must land on the same vector.

Which vector is $Av$?