(Solved): Assume that \( T \) is a linear transformation. Find the standard matrix of \( T \). T \( \mathbb{R ...

Assume that \( T \) is a linear transformation. Find the standard matrix of \( T \). T \( \mathbb{R}^{2} \rightarrow \mathbb{R}^{2} \) is a vertical shear transformation that maps \( e_{1} \) into \( e_{1}-12 e_{2} \) but leaves the vector \( e_{2} \) unchanged.