[See Solution] Assume that T is a linear transformation. Find the standard matrix of T. T: R^2 \rightarrow R^4, T(e_1)=(3,1,3,1) \text , and T(e_2)=(-5,2,0,0) where
Question: Assume that \(T\) is a linear transformation. Find the standard matrix of \(T\).
\[T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{4}, T\left(e_{1}\right)=(3,1,3,1) \text {, and } T\left(e_{2}\right)=(-5,2,0,0)\]where \(e_{1}=(1,0)\) and \(e_{2}=(0,1)\)
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