I am having difficulty solve this problem in my homework:
(In my notation, $[x;y]$ represents a matrix of 2 rows, 1 column)
Let $\mathbf{x}=[x_1;x_2]$, $v_1$=[−3;5] and $v_2=[7;−2]$ and let $T\colon\mathbb{R}^2\to\mathbb{R}^2$ be a linear transformation that maps $\mathbf{x}$ into $x_1v_1+x_2v_2$. Find a matrix $A$ such that $T(\mathbf{x})$ is $A\mathbf{x}$ for each $\mathbf{x}$.
I am pretty clueless. So I assume that I start off with the following:
$x_1v_1 + x_2v_2 = x_1[−3;5] + x_2[7;−2]$
But I do not know what to do from here, or if this is even the correct start!