Is the composition T1 o T2 also well defined? Why or why not? Use the definition of a composition directly to find (T2 o T1)((x,y)). Use (c) to find [T2 • T1]. b. с. d. Form [T2] and [Ti] and compute the matrix product [T2][T1]. е. Verify that [T2][T1] = [T2 • T1].

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 20EQ
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3.3 #5

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Please answer b, c, d and e

 

5.
Let T1 : R² → Rª, and T2 : Rª → R³ be given by:
Ti(х, у)) 3 (3x - 2у, 5х + у, -х + Зу, 4у), and
Т:((х1, х2, хз, х4)) — (3х1 — 5х4, 7x2 + 2хз — х4, 6хз + 9х4).
Transcribed Image Text:5. Let T1 : R² → Rª, and T2 : Rª → R³ be given by: Ti(х, у)) 3 (3x - 2у, 5х + у, -х + Зу, 4у), and Т:((х1, х2, хз, х4)) — (3х1 — 5х4, 7x2 + 2хз — х4, 6хз + 9х4).
b.
Is the composition T1 o T2 also well defined? Why or why not?
Use the definition of a composition directly to find (T2 • T1)((x,y)).
с.
d.
Use (c) to find [T2 • T1].
Form [T2] and [T1] and compute the matrix product [T2][Ti].
е.
Verify that [T2][T1] = [T2 • T1].
Transcribed Image Text:b. Is the composition T1 o T2 also well defined? Why or why not? Use the definition of a composition directly to find (T2 • T1)((x,y)). с. d. Use (c) to find [T2 • T1]. Form [T2] and [T1] and compute the matrix product [T2][Ti]. е. Verify that [T2][T1] = [T2 • T1].
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