A First Course in Linear Algebra · Problem MR.C21

Representations — Robert Beezer

Mathematics — Linear Algebra · matrix-representations-computation

Problem

Find a matrix representation of the linear transformation

T

relative to the bases

B

and

C

T: P_2 \to \mathbb{C}^2, \quad T(p(x)) = \begin{bmatrix}p(1)\\p(3)\end{bmatrix}

B = \left\{2 - 5x + x^2,\, 1 + x - x^2,\, x^2\right\}

C = \left\{\begin{bmatrix}3\\4\end{bmatrix}, \begin{bmatrix}2\\3\end{bmatrix}\right\}