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Math / Linear Algebra and Its Applications 5 / Chapter 1.9 / Problem 5E

Linear Algebra and Its Applications | 5th Edition | ISBN: 9780321982384 | Authors: David C. Lay; Steven R. Lay; Judi J. McDonald

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In Exercises, assume that T is a linear transformation.

Chapter 1, Problem 5E

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QUESTION:

In Exercises, assume that T is a linear transformation. Find the standard matrix of T.

\(T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}\) is a vertical shear transformation that maps \(e_1\) into \(\mathbf{e}_{1}-2 \mathbf{e}_{2}\) but leaves the vector \(e_2\) unchanged.

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QUESTION:

In Exercises, assume that T is a linear transformation. Find the standard matrix of T.

\(T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}\) is a vertical shear transformation that maps \(e_1\) into \(\mathbf{e}_{1}-2 \mathbf{e}_{2}\) but leaves the vector \(e_2\) unchanged.

ANSWER:

Solution:

Step 1 of 1

Here

$T({e}_{1})={e}_{1}-2{e}_{2}$

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