1.Determine by inspection why the given set S is not a basis for R^3. (That is, either S is linearly dependent or S does not span R^3 S = {u1, u5} 2.Use theorem 9, property 3 to determine whether the given set is a basis for the indicated vector space. (Theorem 9, property 3: Let W be a subspace of R^n with dim(W)=p; any set p linearly independent vectors in W is a basis for W ) S = {v1, v2, v4} for R3

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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1.Determine by inspection why the given set S is not a basis for R^3. (That is, either S is linearly dependent or S does not span R^3

S = {u1, u5}

2.Use theorem 9, property 3 to determine whether the given set is a basis for the indicated vector space.

(Theorem 9, property 3: Let W be a subspace of R^n with dim(W)=p; any set p linearly independent vectors in W is a basis for W )

S = {v1, v2, v4} for R3

 

--[(}]· --|· --[+]
U₁ =
=
=
2
1
3
--[8] --B----]
U4 =
V₁
3
0
1
=
---
V3 =
2
1
0
V4
1
-1
3
3
(15)
Transcribed Image Text:--[(}]· --|· --[+] U₁ = = = 2 1 3 --[8] --B----] U4 = V₁ 3 0 1 = --- V3 = 2 1 0 V4 1 -1 3 3 (15)
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