u=2i+j, v= i+j, and w= i-j. u = av +bw where a and b are scalars. find a and b.
I have tried a buttload of numbers and none seem to work because one when I add them together to form u one is negative and there is no negative in u.
Note that $\displaystyle x\mathbf{i}+y\mathbf{j}=\left<x,y\right>$ (just thought I would mention that, just in case my notation confused you).
Plug the vectors into the equation to get
$\displaystyle \left<2,1\right>=a\left<1,1\right>+b\left<1,-1\right>\implies \left<2,1\right>=\left<a+b,a-b\right>$
Therefore, $\displaystyle a+b=2$ and $\displaystyle a-b=1$.
Can you solve these for a and b?