A First Course in Linear Algebra · Problem SLT-C20

Linear Transformations — Robert Beezer

Mathematics — Linear Algebra · surjective-linear-transformations

Problem

Example SAR concludes with an expression for a vector

\mathbf{u} \in \mathbb{C}^5

that we believe will create the vector

\mathbf{v} \in \mathbb{C}^5

when used to evaluate

T

. That is,

T(\mathbf{u}) = \mathbf{v}

. Verify this assertion by actually evaluating

T

with

\mathbf{u}

. If you do not have the patience to push around all these symbols, try choosing a numerical instance of

\mathbf{v}

, compute

\mathbf{u}

, and then compute

T(\mathbf{u})

, which should result in

\mathbf{v}