This is the text I've been given for the test:
Let L be a linear map $\mathbb {R}^2 \to \mathbb{R}^2$, whose matrix respect to the standard basis is:
[L] = \begin{bmatrix} 1 & -1 \\[0.3em] -1 & 0 \\[0.3em] \end{bmatrix}
Now, consider the following two bases of $\mathbb R^2$:
$\beta$ V1 = \begin{bmatrix} 0 \\[0.3em] 1 \\[0.3em] \end{bmatrix}
$\beta$ v2 = \begin{bmatrix} , 1 \\[0.3em] 1 \\[0.3em] \end{bmatrix}
and
$\gamma$ w1 = \begin{bmatrix} , 1 \\[0.3em] 2 \\[0.3em] \end{bmatrix}
$\gamma$ w2 = \begin{bmatrix} , 0 \\[0.3em] 1 \\[0.3em] \end{bmatrix}
Command: write the associated matrix L with respect at base $\beta$ (domain) to $\gamma$ (codomain).
Solution: \begin{bmatrix} -1 & 0 \\[0.3em] 2 & -1 \\[0.3em] \end{bmatrix}
I thought i could write (1,0) as the difference between v1 and v2, but then i don't when or how to use it. I'm pretty confused on how i should relate the first matrix with the two basis!
