A First Course in Linear Algebra · Problem SLT-C24

Linear Transformations — Robert Beezer

Mathematics — Linear Algebra · surjective-linear-transformations

Problem

Determine whether or not the linear transformation

T: P_3 \to \mathbb{C}^5

below is surjective:

T\left(a + bx + cx^2 + dx^3\right) = \begin{bmatrix} a+b \\ b+c \\ c+d \\ a+c \\ b+d \end{bmatrix}