A First Course in Linear Algebra · Problem VR-C10

Representations — Robert Beezer

Mathematics — Linear Algebra · vector-representations

Problem

In the vector space

\mathbb{C}^3

, compute the vector representation

\rho_B(\mathbf{v})

for the basis

B

and vector

\mathbf{v}

below.

B = \left\{\begin{bmatrix} 2 \\ -2 \\ 2 \end{bmatrix}, \begin{bmatrix} 1 \\ 3 \\ 1 \end{bmatrix}, \begin{bmatrix} 3 \\ 5 \\ 2 \end{bmatrix}\right\} \qquad \mathbf{v} = \begin{bmatrix} 11 \\ 5 \\ 8 \end{bmatrix}