Finding Standard Matrices of Linear Transformations

The problem has three separate parts (the codomain labels for parts 2 and 3 are printed as $\mathbb{R}^4$, but the descriptions are the standard $2\times2$ transformations; see notes below). Part 1: $T:\mathbb{R}^2\to\mathbb{R}^4$, with - $T(\mathbf{e}1)=(3,1,3,1)$ - $T(\mathbf{e}2)=(-5,2,0,0)$ -...