Question 1 Let U = Span and W Span be subspaces of R³. Find bases for U +W and Un WW.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Question 1
Let U
Span
and W =
Span
be subspaces of R³. Find
bases for U +W and Un WW.
Question 2
Let B
{V1, V2, ..., Vn} be a basis for a vector space V and define vn+1 € V by
Vn+1 = A1V1 + a2V2 + . . . + anVn, where a, E R and a; # 0 for i = 1, 2, ... , n.
i. Prove: C = {v2, V3, . . , vn, Vn+1} is a basis for V.
Fix the given order of vectors, that is, B = (v1, V2, ... , Vn) and C = (v2, V3, . .. , Vn, Vn+1)
so that henceforth these are ordered bases of V.
ii. Find [1].
iii. Find det [I]:
Transcribed Image Text:Question 1 Let U Span and W = Span be subspaces of R³. Find bases for U +W and Un WW. Question 2 Let B {V1, V2, ..., Vn} be a basis for a vector space V and define vn+1 € V by Vn+1 = A1V1 + a2V2 + . . . + anVn, where a, E R and a; # 0 for i = 1, 2, ... , n. i. Prove: C = {v2, V3, . . , vn, Vn+1} is a basis for V. Fix the given order of vectors, that is, B = (v1, V2, ... , Vn) and C = (v2, V3, . .. , Vn, Vn+1) so that henceforth these are ordered bases of V. ii. Find [1]. iii. Find det [I]:
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