A First Course in Linear Algebra · Problem MR.RQ.2

Representations — Robert Beezer

Mathematics — Linear Algebra · matrix-representations-computation

Problem

Find the matrix representation,

M^T_{B,C}

of the linear transformation

T: \mathbb{C}^2 \to \mathbb{C}^2, \quad T\left(\begin{bmatrix}x_1\\x_2\end{bmatrix}\right) = \begin{bmatrix}2x_1 - x_2\\ 3x_1 + 2x_2\end{bmatrix}

relative to the bases

B = \left\{\begin{bmatrix}2\\3\end{bmatrix}, \begin{bmatrix}-1\\2\end{bmatrix}\right\} \qquad C = \left\{\begin{bmatrix}1\\0\end{bmatrix}, \begin{bmatrix}1\\1\end{bmatrix}\right\}