I have the problem below here:
In Exercise 1 and 2 let $T: \Bbb R^{2} \to \Bbb R^{2}$ be the linear operator whose standard matrix $[T]$ is given. Find the matrix $[T]_B$ with respect to the basis $B = \{\mathbf v_1, \mathbf v_2\}$, and verify that Formula (7) holds for every vector $x$ in $\Bbb R^{2}$. $$ T = \pmatrix{1& -1\\1&1}; \quad \mathbf v_1 = \pmatrix{1\\1}, \quad \mathbf v_2 = \pmatrix{-1\\0}. $$
How should i compute this ?
$A:=[v_1\,v_2]$ then $A^{-1}TA=M_B$
$$\begin{bmatrix} 0 & 1\\ -1 & 1 \end{bmatrix}\begin{bmatrix} 1 & -1\\ 1 & 1 \end{bmatrix}\begin{bmatrix} 1 & -1\\ 1 & 0 \end{bmatrix}=\begin{bmatrix} 2 & -1\\ 2 & 0 \end{bmatrix}=M_B$$