A First Course in Linear Algebra · Problem ILT-C29

Linear Transformations — Robert Beezer

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

Problem

Let

A = \begin{bmatrix} 1 & 2 & 1 & 1 \\ 2 & 1 & 1 & 0 \\ 1 & 2 & 1 & 2 \\ 1 & 2 & 1 & 1 \end{bmatrix}

and let

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

be given by

T(\mathbf{x}) = A\mathbf{x}

. Find

\mathcal{K}(T)

. Is

T

injective?