#### Answer

$[3,-2,3]$

#### Work Step by Step

We compute the vector $2a+3c$ by computing the value of each of its components.
The first component $x_1 = 2 (0) + 3 (1) = 3$, the second, $x_2 = 2 (2) + 3 (-2) = -2$, the third, $x_3 = 2(0) + 3(1) = 3$.
Grouping each of these components as one vector, we find that $2a+3c = [x_1, x_2, x_3] = [3, -2, 3]$.