4 b, c, and a please 4. You are given a linear transformation f : R? → R² such that2f1(a)for f. It not, explain why this is impossible.(b)assume f is such an orthogonal projection and find a possible matrix for f. If not, explainwhy this is impossible.(c)a reflection and find a possible matrix for f. If not, explain why this is impossible.Could f be a rotation? If so, assume f is a rotation and find a possible matrixCould f be an orthogonal projection onto a line through the origin? If so,Could f be a reflection about a line through the origin? If so, assume f is such

Answered: 4. You are given a linear…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Related questions

Question

4 b, c, and a please

4. You are given a linear transformation f : R? → R² such that
2
f
1
(a)
for f. It not, explain why this is impossible.
(b)
assume f is such an orthogonal projection and find a possible matrix for f. If not, explain
why this is impossible.
(c)
a reflection and find a possible matrix for f. If not, explain why this is impossible.
Could f be a rotation? If so, assume f is a rotation and find a possible matrix
Could f be an orthogonal projection onto a line through the origin? If so,
Could f be a reflection about a line through the origin? If so, assume f is such

Expert Solution

Rotation

Since you have asked multiple questions, we will solve the first question for you. If you want any
specific question to be solved, then please specify the question number or post only that question.

Given linear transformation is $f : ℝ^{2} \to ℝ^{2}$ such that $f ([\begin{matrix} 2 \\ 1 \end{matrix}]) = [\begin{matrix} - 1 \\ 2 \end{matrix}]$ .

(a)

A linear transformation $f : ℝ^{2} \to ℝ^{2}$ is said to be rotation transformation, if for some $θ$ and $[\begin{matrix} x \\ y \end{matrix}] \in ℝ^{2}$ , it satisfies: