A First Course in Linear Algebra · Problem ILT-C26

Linear Transformations — Robert Beezer

Mathematics — Linear Algebra · injective-linear-transformations

Problem

Let

A = \begin{bmatrix} 1 & 2 & 3 & 1 & 0 \\ 2 & -1 & 1 & 0 & 1 \\ 1 & 2 & -1 & -2 & 1 \\ 1 & 3 & 2 & 1 & 2 \end{bmatrix}

and let

T: \mathbb{C}^5 \to \mathbb{C}^4

be given by

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

. Is

T

injective? (Hint: No calculation is required.)