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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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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