Linear Algebra and Its Applications (5th Edition)

Published by Pearson
ISBN 10: 032198238X
ISBN 13: 978-0-32198-238-4

Chapter 5 - Eigenvalues and Eigenvectors - 5.4 Exercises - Page 295: 3

Answer

See solution below

Work Step by Step

a) $T(\vec{e_1})=-\vec{b_2}+\vec{b_3}$ $T(\vec{e_2})=-\vec{b_1}-\vec{b_3}$ $T(\vec{e_3})=\vec{b_1}-\vec{b_2}$ b) $[T(\vec{e_1})]_B=\begin{bmatrix} 0\\ -1\\ 1 \end{bmatrix}$, $[T(\vec{e_2})]_B=\begin{bmatrix} -1\\ 0\\ -1 \end{bmatrix}$, and $[T(\vec{e_3})]_B=\begin{bmatrix} 1\\ -1\\ 0 \end{bmatrix}$ c) The matrix T relative to $E$ and $B$ is $\begin{bmatrix} 0&-1&1\\ -1&0&-1\\ 1&-1&0 \end{bmatrix}$
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