A First Course in Linear Algebra · Problem ILT-C30

Linear Transformations — Robert Beezer

Mathematics — Linear Algebra · kernel-injective-linear-transformations

Problem

Let

T: M_{22} \to P_2

be given by

T\begin{pmatrix} \begin{bmatrix} a & b \\ c & d \end{bmatrix} \end{pmatrix} = (a+b) + (a+c)x + (a+d)x^2

. Is

T

injective? Find

\mathcal{K}(T)