Let u, v, and w be vectors in R and let c and d be scalars. ThenCommutativityAssociativitya. u + v = v +ub. (u + v) + w = u + (v + w)C. u + 0 = Ud. u + (-u) = 0e. c(u + v) = cu + cvf. (c + d)u = cu + dug. c(du) = (cd) uh. 1u = uDistributivityDistributivitySimplify the given vector expression. Indicate which properties in the theorem above you use.2(a - 4b) + 4(2b + a)2(a 4b) + 4(2b + a) = (2a - 8b) + (8b + 4a)= (2a + 4a) + (8b - 8b)= 6aproperties ?properties?

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2(a 4b) + 4(2b + a) 2(a 4b) + 4(2b + a) = (2a - 8b) + (8b + 4a) = (2a + 4a) + (8b - 8b) = 6a properties properties ? ?

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...

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Question

Let u, v, and w be vectors in R and let c and d be scalars. Then
Commutativity
Associativity
a. u + v = v +u
b. (u + v) + w = u + (v + w)
C. u + 0 = U
d. u + (-u) = 0
e. c(u + v) = cu + cv
f. (c + d)u = cu + du
g. c(du) = (cd) u
h. 1u = u
Distributivity
Distributivity
Simplify the given vector expression. Indicate which properties in the theorem above you use.
2(a - 4b) + 4(2b + a)
2(a 4b) + 4(2b + a) = (2a - 8b) + (8b + 4a)
= (2a + 4a) + (8b - 8b)
= 6a
properties ?
properties
?

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