A First Course in Linear Algebra · Problem LT.RQ2

Linear Transformations — Robert Beezer

Mathematics — Linear Algebra · matrix-representation-linear-transformation

Problem

Determine the matrix representation of the linear transformation

S

below.

S: \mathbb{C}^2 \to \mathbb{C}^3, \quad S\left(\begin{bmatrix} x_1 \\ x_2 \end{bmatrix}\right) = \begin{bmatrix} 3x_1 + 5x_2 \\ 8x_1 - 3x_2 \\ -4x_1 \end{bmatrix}