A First Course in Linear Algebra · Problem MR.C25

Representations — Robert Beezer

Mathematics — Linear Algebra · matrix-representations-surjectivity

Problem

Use a matrix representation to determine if the linear transformation

T: P_3 \to M_{22}

is surjective.

T\left(a + bx + cx^2 + dx^3\right) = \begin{bmatrix}-a+4b+c+2d & 4a-b+6c-d\\ a+5b-2c+2d & a+2c+5d\end{bmatrix}