Assume that T is a linear transformation. Find the standard matrix of T. T: R² R², first performs a horizontal shear that transforms e into e +6e₁ (leaving e₁ unchanged) and then reflects points through the line x₂ = -x₁.
Assume that T is a linear transformation. Find the standard matrix of T. T: R² R², first performs a horizontal shear that transforms e into e +6e₁ (leaving e₁ unchanged) and then reflects points through the line x₂ = -x₁.
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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PLease do BOTH!!! PLEASE!!!

Transcribed Image Text:Assume that T is a linear transformation. Find the standard matrix of T.
T: R² →R², first performs a horizontal shear that transforms e2 into e2
points through the line x₂ = -X₁.
A =
(Type an integer or simplified fraction for each matrix element.)
+6e₁ (leaving e₁ unchanged) and then reflects

Transcribed Image Text:Describe the possible echelon forms of the standard matrix for a linear transformation T where T: R³ R4 is one-to-one.
Give some examples of the echelon forms. The leading entries, denoted, may have any nonzero value. The
starred entries, denoted *, may have any value (including zero). Select all that apply.
0
0
0
0
0
0
0
0
0 0
0
0
*
0
0
B.
ui
*
0
00
0
0
00
*
C.
F.
*
00
000
0
0
0 00
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