Exercise 19

Let $\vv = \langle 1, -2 \rangle$, $\vu = \langle 0, 4 \rangle$, and $\vw = \langle -5, 7 \rangle$.

1. Determine the components of the vector $\vu - \vv$.

2. Determine the components of the vector $2\vv - 3\vu$.

3. Determine the components of the vector $\vv + 2\vu - 7 \vw$.

4. Determine scalars $a$ and $b$ such that $a \vv + b\vu = \vw$. Show all of your work in finding $a$ and $b$.