-0 V₁ = V2 = [f] = = 1 7 1 -3 1 "-(⠀) -1 -3 2 -1 -32, Find the image vectors f (v₁), f (v₂), f (√3) form a basis of R3 (b) Consider a linear map ƒ : R³ → R3 and suppose the matrix associated with ƒ under the standard basis of R3 is given by: V3 = 1

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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2. (a) Show that the set B = (v1, V2, V3) defined by:
1
0
V₁
[f]
2 =
=
form a basis of R3
(b) Consider a linear map f: R³ → R³ and suppose the matrix associated with f under the
standard basis of R3 is given by:
1
-1
-1
1
2
Find the image vectors f (v₁), f (v₂), f (√3)
1
*-()
1
2
-3 1
-3 2
-3 2
Transcribed Image Text:2. (a) Show that the set B = (v1, V2, V3) defined by: 1 0 V₁ [f] 2 = = form a basis of R3 (b) Consider a linear map f: R³ → R³ and suppose the matrix associated with f under the standard basis of R3 is given by: 1 -1 -1 1 2 Find the image vectors f (v₁), f (v₂), f (√3) 1 *-() 1 2 -3 1 -3 2 -3 2
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