T([0])=[1.17] Check Answer and then rotates points about the origin by 4 radians.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 45EQ
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11) Please show all work and explain. I am a bit confused about linear transformations, so if you can be as clear as possible, it would be appreciated.
![Find the standard matrix for the linear transformation \( T: \mathbb{R}^2 \rightarrow \mathbb{R}^2 \) that shears vertically, with
\[
T \left( \begin{bmatrix} 1 \\ 0 \end{bmatrix} \right) = \begin{bmatrix} 1 \\ 1.17 \end{bmatrix}
\]
and then rotates points about the origin by \( \frac{\pi}{4} \) radians.
\[
\begin{bmatrix}
\boxed{\phantom{a}} & \boxed{\phantom{a}} \\
\boxed{\phantom{a}} & \boxed{\phantom{a}}
\end{bmatrix}
\]
[Check Answer]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd2a99bde-e99a-4ca5-bad3-91849c93fae5%2Fa2cf8b26-4ec7-4eaf-a3d4-76c001be4140%2Fs6s829y_processed.png&w=3840&q=75)
Transcribed Image Text:Find the standard matrix for the linear transformation \( T: \mathbb{R}^2 \rightarrow \mathbb{R}^2 \) that shears vertically, with
\[
T \left( \begin{bmatrix} 1 \\ 0 \end{bmatrix} \right) = \begin{bmatrix} 1 \\ 1.17 \end{bmatrix}
\]
and then rotates points about the origin by \( \frac{\pi}{4} \) radians.
\[
\begin{bmatrix}
\boxed{\phantom{a}} & \boxed{\phantom{a}} \\
\boxed{\phantom{a}} & \boxed{\phantom{a}}
\end{bmatrix}
\]
[Check Answer]
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