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.
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$\begingroup$ 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 $\left[ 1 \ -1 \right]$. $\endgroup$– Aniruddha DeshmukhMar 9, 2020 at 2:29
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$\begingroup$ Isn't that the answer I've used (-1,1). $\endgroup$– pashaMar 9, 2020 at 2:42
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$\begingroup$ Nvm I'm an idiot. $\endgroup$– pashaMar 9, 2020 at 2:55
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1 Answer
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My calculations were off. I was calculating the negative of the answer.
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 $$ [a,b]= [1,-1] $$