Let W be the subspace of R³ spanned by the vectors =(1,2,3,-1.2) and v= (2,4.7.2.-1). A basis of the orthogonal complement W of W is ... A ((1,0,0,0,0), (0,1,0,0,0).(0,0,1,0,0)) B. ((-17,0,5,0,1), (13,0,-4,1,0). (2,-1,0,0,0)) C. {(2,-1,0,0,0). (13,0,-4.1,0). (1,0,0,0,0)) D. ((1,2,3,-1,2). (2,4,7,2,1),(2,-1,0,0,0)) E. None in the given list

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
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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Let W be the subspace of RS spanned by the vectors = (1,2,3,-1,2) and v= (2,4,7,2, -1). A basis of the orthogonal complement
W of W is
.....
A. {(1,0,0,0,0), (0,1,0,0,0), (0,0,1,0,0))
B. ((-17,0,5,0,1), (13,0, -4,1,0), (2,-1,0,0,0))
C. {(2,1,0,0,0), (13,0, -4,1,0), (1,0,0,0,0))
D. {(1,2,3,-1,2). (2,4,7,2,1),(2,-1,0,0,0))
E. None in the given list
Transcribed Image Text:Let W be the subspace of RS spanned by the vectors = (1,2,3,-1,2) and v= (2,4,7,2, -1). A basis of the orthogonal complement W of W is ..... A. {(1,0,0,0,0), (0,1,0,0,0), (0,0,1,0,0)) B. ((-17,0,5,0,1), (13,0, -4,1,0), (2,-1,0,0,0)) C. {(2,1,0,0,0), (13,0, -4,1,0), (1,0,0,0,0)) D. {(1,2,3,-1,2). (2,4,7,2,1),(2,-1,0,0,0)) E. None in the given list
Expert Solution
Step 1

Let W be a subspace of a vector space V. Then orthogonal complement of W is defined as,

W={u| vW and u.v=0}

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