Consider the subspaces of R5 U = span {⃗u1 = (1, 3, −2, 2, 3), ⃗u2 = (1, 4, −3, 4, 2), ⃗u3 = (2, 3, −1, −2, 9)} V = span {⃗v1 = (1, 3, 0, 2, 1), ⃗v2 = (1, 5, −6, 6, 3), ⃗v3 = (2, 5, 3, 2, 1)} Find the dimension of and a basis of U + V.

Consider the subspaces of R5 U = span {⃗u1 = (1, 3, −2, 2, 3), ⃗u2 = (1, 4, −3, 4, 2), ⃗u3 = (2, 3, −1, −2, 9)} V = span {⃗v1 = (1, 3, 0, 2, 1), ⃗v2 = (1, 5, −6, 6, 3), ⃗v3 = (2, 5, 3, 2, 1)} Find the dimension of and a basis of U + V.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.5: Basis And Dimension

Problem 65E: Find a basis for the vector space of all 33 diagonal matrices. What is the dimension of this vector...

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Question

Consider the subspaces of R⁵
U = span {⃗u1 = (1, 3, −2, 2, 3), ⃗u2 = (1, 4, −3, 4, 2), ⃗u3 = (2, 3, −1, −2, 9)}
V = span {⃗v1 = (1, 3, 0, 2, 1), ⃗v2 = (1, 5, −6, 6, 3), ⃗v3 = (2, 5, 3, 2, 1)}

Find the dimension of and a basis of U + V.

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