Let U = span{(1,1, 1), (1, 1, 0)} C R°, V = span{(1,2, 0), (1, –1,0)} C R°, and let W = span{(1, 1, 1), (1, 1,0), (1, 2, 0), (1, –1,0)}. Find the dimensions of U, V, W,U n V and verify that dim(W) dim(U) + dim(V) – dim(U nV). You must explain your reasoning clearly at cach stage of the calcula- tion.

Let U = span{(1,1, 1), (1, 1, 0)} C R°, V = span{(1,2, 0), (1, –1,0)} C R°, and let W = span{(1, 1, 1), (1, 1,0), (1, 2, 0), (1, –1,0)}. Find the dimensions of U, V, W,U n V and verify that dim(W) dim(U) + dim(V) – dim(U nV). You must explain your reasoning clearly at cach stage of the calcula- tion.

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

Let U = span{(1,1, 1), (1, 1, 0)} C R*, V = span{(1,2,0), (1, –1,0)} C
R*, and let W = span{(1,1,1), (1, 1,0), (1, 2, 0), (1, –1, 0)}.
Find the dimensions of U, V, W,U n V and verify that dim(W) :
dim(U) + dim(V) – dim(U n V).
%3D
You must explain your reasoning clearly at cach stage of the calcula-
tion.

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