A First Course in Linear Algebra · Problem SLT-C23

Linear Transformations — Robert Beezer

Mathematics — Linear Algebra · surjective-linear-transformations

Problem

Determine whether or not the following linear transformation

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

is surjective:

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