Linear Algebra and Its Applications (5th Edition)

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

Chapter 1 - Linear Equations in Linear Algebra - 1.8 Exercises - Page 69: 1

Answer

$T(\vec{u})=\begin{bmatrix}2\\-6\end{bmatrix}$ $T(\vec{v})=\begin{bmatrix}2a\\2b\end{bmatrix}$

Work Step by Step

$T(\vec{u})=\mathbf{A}\vec{u}=\begin{bmatrix}2&0\\0&2\end{bmatrix}\begin{bmatrix}1\\-3\end{bmatrix}=\begin{bmatrix}2\cdot1+0\cdot(-3)\\0\cdot1+2\cdot(-3)\end{bmatrix}$ $T(\vec{v})=\mathbf{A}\vec{v}=\begin{bmatrix}2&0\\0&2\end{bmatrix}\begin{bmatrix}a\\b\end{bmatrix}=\begin{bmatrix}2\cdot a+0\cdot b\\0 \cdot a+2\cdot b\end{bmatrix}$
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