(4) (2 points) Let $T: \mathbb{R}^n \to \mathbb{R}^n$ denote a linear transformation, and let A denote its standard matrix (this means $T(x) = Ax$ for all n-dimensional column vectors x in $\mathbb{R}^n$). If $\beta$ denotes the standard basis {$e_1, e_2, ..., e_n$} for $\mathbb{R}^n$, then show that the $\beta$-matrix for T is equal to A the standard matrix for T.
