Express $\langle 4, -8 \rangle$ as a linear combination of $\vec{u}$ and $\vec{v}$, given $\vec{u}=\langle 1,1 \rangle$ and $\vec{v}=\langle -1,1 \rangle$.

So, I set up: $\vec{i}=\langle 1,0 \rangle$ and $\vec{j}=\langle 0,1 \rangle \implies$

$$A(-\vec{i}+\vec{j})+B(\vec{i}+\vec{j})=4\vec{i}-8\vec{j}$$

This looks to be impossible to find values of $A$ and $B$ which satisfy this equality.