A First Course in Linear Algebra · Problem MR.C52

Representations — Robert Beezer

Mathematics — Linear Algebra · kernel-matrix-representation

Problem

Find a basis for the kernel of the linear transformation

T: P_2 \to M_{22}

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