Let B = [1, U] be a base for V=R², where u = (1,2) and =(-1,1). We know that everyvector in V is a linear combination of u and . That is,w = au + Bv,where a and 3 are scalars. If = (6,0), what are the values of a and 3?B=2a = 4B = -4a = -4a = -2OB=4a = 2B = -2

Here, w=αu+βv⇒(6,0)=α(1,2)+β(-1,1)⇒(6,0)=(α-β,2α+β) Comparing the components of vectors:…

U Let B= [u, be a base for V=R2, where u = (1, 2) and = (-1,1). We know that every vector in V is a linear combination of u and e. That is, w = ou + Bu, where and are scalars. If = (6,0), what are the values of a and 3? B=2 a = 4 B = -4 a = -4 a = -2 B = 4 a=2 B = -2

U Let B= [u, be a base for V=R2, where u = (1, 2) and = (-1,1). We know that every vector in V is a linear combination of u and e. That is, w = ou + Bu, where and are scalars. If = (6,0), what are the values of a and 3? B=2 a = 4 B = -4 a = -4 a = -2 B = 4 a=2 B = -2

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.3: Subspaces Of Vector Spaces

Problem 52E

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Question

Let B = [1, U] be a base for V=R², where u = (1,2) and =(-1,1). We know that every
vector in V is a linear combination of u and . That is,
w = au + Bv,
where a and 3 are scalars. If = (6,0), what are the values of a and 3?
B=2
a = 4
B = -4
a = -4
a = -2
OB=4
a = 2
B = -2

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