7. Let f: R? → R² and g: R² → R² be defined as the matrix multiplication (E) - 6 =)A (E) (E) - 1 f 2 1 5 (a) Show that fog:R² → R² satisfies f og {} f-(X) = {T}: (b) Let X Show that 1 (c) Use part (b) to show that ƒ is injective.
7. Let f: R? → R² and g: R² → R² be defined as the matrix multiplication (E) - 6 =)A (E) (E) - 1 f 2 1 5 (a) Show that fog:R² → R² satisfies f og {} f-(X) = {T}: (b) Let X Show that 1 (c) Use part (b) to show that ƒ is injective.
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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Transcribed Image Text:7. Let f: R? → R² and g: R² → R² be defined as the matrix multiplication
(E) - 6 =)A
(E)
(E) - 1
f
2
1 5
(a) Show that fog:R² → R² satisfies f og
{}
f-(X) = {T}:
(b) Let X
Show that
1
(c) Use part (b) to show that ƒ is injective.
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