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T([0])=[1.17] Check Answer and then rotates points about the origin by 4 radians.

T([0])=[1.17] Check Answer and then rotates points about the origin by 4 radians.

Linear Algebra: A Modern Introduction
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]
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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