If {v, w} is independent, find conditions on the scalars k1 and k2 so that the set {k,v + w, v + k2w} is also independent. (a) k1 + k2 = 1 (b) k1 + k2 # 1 (c) ki # k2 (d) k¡k2 =1 (e) kįk2 # 1

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter2: Matrices
Section2.2: Properties Of Matrrix Operations
Problem 57E
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If {v, w} is independent, find conditions on the scalars k1 and k2 so that the set
{k,v + w, v + k2w} is also independent.
(a) k1 + k2 = 1 (b) k1 + k2 # 1 (c) ki # k2 (d) k¡k2 =1 (e) kįk2 # 1
Transcribed Image Text:If {v, w} is independent, find conditions on the scalars k1 and k2 so that the set {k,v + w, v + k2w} is also independent. (a) k1 + k2 = 1 (b) k1 + k2 # 1 (c) ki # k2 (d) k¡k2 =1 (e) kįk2 # 1
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