(b) Consider a linear map f: R³ R3 and suppose the matrix associated with f under the standard basis of R3 is given by: [f] = -1 1 Find the image vectors f (v₁), f (v₂), f (√3) -3 1 -3 2 -3 2

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.3: Spanning Sets And Linear Independence
Problem 30EQ
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just b)

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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