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]

Linear transformation and associated matrix

Answered: T([0])=[1.17] Check Answer and then…

Math

Advanced Math

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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Question

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]

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