Linear Algebra and Its Applications (5th Edition)

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

Chapter 1 - Linear Equations in Linear Algebra - 1.9 Exercises - Page 79: 6

Answer

See explanation

Work Step by Step

$T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ is a horizontal shear transformation that leaves $\mathbf{e}_{1}$ unchanged and maps $\mathbf{e}_{2}$ into $\mathbf{e}_{2}+3 \mathbf{e}_{1}$ Given Question \[ \begin{array}{c} T\left(e_{1}\right)=e \\ T\left(e_{2}\right)=e_{2}+3 e_{1}=\left[\begin{array}{c} 3 \\ 1 \end{array}\right] \\ A=\left[\begin{array}{cc} 1 & 3 \\ 0 & 1 \end{array}\right] \end{array} \] Standard matrix
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