A First Course in Linear Algebra · Problem SLT-C28

Linear Transformations — Robert Beezer

Mathematics — Linear Algebra · range-surjective-linear-transformations

Problem

Let

T: \mathbb{C}^4 \to M_{22}

be given by

T\left(\begin{bmatrix} a \\ b \\ c \\ d \end{bmatrix}\right) = \begin{bmatrix} a+b & a+b+c \\ a+b+c & a+d \end{bmatrix}

. Find a basis of

\mathcal{R}(T)

. Is

T

surjective?