A First Course in Linear Algebra · Problem MR.C20

Representations — Robert Beezer

Mathematics — Linear Algebra · matrix-representations-computation

Problem

Compute the matrix representation of

T

relative to the bases

B

and

C

T: P_3 \to \mathbb{C}^3, \quad T\left(a + bx + cx^2 + dx^3\right) = \begin{bmatrix}2a - 3b + 4c - 2d\\ a + b - c + d\\ 3a + 2c - 3d\end{bmatrix}

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