# Find the coordinates of the vector $\vec x =[5,0]$ relative to the basis $B$

Following is a homework question. My answer $$[-1,1]$$ is wrong even though I already verified $$(-1)[-5,-6] + [-10,-6]$$ is $$[5,0]$$. I checked stack exchange and it seems like I have the approach. What am I doing wrong?

Edit: Fixed the typo.

• If you have verified that $\left[ 5 \ 0 \right] = \left( -1 \right) \left[ -5 \ -6 \right] + \left( 1 \right) \left[ -10 \ -6 \right]$, then the coordinates relative to the basis would be $\left[ -1 \ 1 \right]$ and not $\left[ 1 \ -1 \right]$. Mar 9, 2020 at 2:29
• Isn't that the answer I've used (-1,1). Mar 9, 2020 at 2:42
• Nvm I'm an idiot. Mar 9, 2020 at 2:55

To solve the question, all you need to do is create two multipliers $$a,b$$. $$a\cdot[-5,-6] + b\cdot[-10,-6] = [5,0]\\ -5a-10b=5 \\ -6a-6b=0$$ which gives $$[a,b]= [1,-1]$$