1. ## vector mutiplication.

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.

2. Originally Posted by hotdogking
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 $x\mathbf{i}+y\mathbf{j}=\left$ (just thought I would mention that, just in case my notation confused you).

Plug the vectors into the equation to get

$\left<2,1\right>=a\left<1,1\right>+b\left<1,-1\right>\implies \left<2,1\right>=\left$

Therefore, $a+b=2$ and $a-b=1$.

Can you solve these for a and b?