A First Course in Linear Algebra · Problem LT.RQ1

Linear Transformations — Robert Beezer

Mathematics — Linear Algebra · linear-transformations

Problem

Is the function below a linear transformation? Why or why not?

T: \mathbb{C}^3 \to \mathbb{C}^2, \quad T\left(\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}\right) = \begin{bmatrix} 3x_1 - x_2 + x_3 \\ 8x_2 - 6 \end{bmatrix}