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)ucu + du g. c(du) = (cd)u h. 1u - u Commutativity Associativity Distributivity Distributivity nplify the given vector expression. Indicate which properties in the theorem 3(a - 5b) + 5(3b + a) a − 5b) + 5(3b + a) = (3a − 15b) + (15b + 5a) - (3a + 5a) + (15b − 15b) = 8a properties a. and c. ✔ properties a. and f.

Elementary Linear Algebra (MindTap Course List)
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Author:Ron Larson
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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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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
(cd)u
g. c(du)
h. 1u - u
Simplify the given vector expression. Indicate which properties in the theorem above you use.
3(a - 5b) + 5(3b + a)
3(a - 5b) + 5(3b + a) = (3a - 15b) + (15b + 5a)
=
Distributivity
Distributivity
(3a + 5a) + (15b - 15b)
= 8a
properties a. and c. ✔
properties a. and f. ✔
Transcribed Image Text: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 (cd)u g. c(du) h. 1u - u Simplify the given vector expression. Indicate which properties in the theorem above you use. 3(a - 5b) + 5(3b + a) 3(a - 5b) + 5(3b + a) = (3a - 15b) + (15b + 5a) = Distributivity Distributivity (3a + 5a) + (15b - 15b) = 8a properties a. and c. ✔ properties a. and f. ✔
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