1. **State the problem:** We are given two vectors $\mathbf{v} = [2, -1]$ and $\mathbf{w} = [-3, -2]$. We need to compute the vector sums $\mathbf{v} + \mathbf{w}$ and $\mathbf{v} - \mathbf{w}$. 2. **Recall the formula for vector addition and subtraction:** - Vector addition: $\mathbf{v} + \mathbf{w} = [v_1 + w_1, v_2 + w_2]$ - Vector subtraction: $\mathbf{v} - \mathbf{w} = [v_1 - w_1, v_2 - w_2]$ 3. **Calculate $\mathbf{v} + \mathbf{w}$:** $$\mathbf{v} + \mathbf{w} = [2 + (-3), -1 + (-2)] = [-1, -3]$$ 4. **Calculate $\mathbf{v} - \mathbf{w}$:** $$\mathbf{v} - \mathbf{w} = [2 - (-3), -1 - (-2)] = [2 + 3, -1 + 2] = [5, 1]$$ 5. **Final answer:** - $\mathbf{v} + \mathbf{w} = [-1, -3]$ - $\mathbf{v} - \mathbf{w} = [5, 1]$