Which of the following statements is (are) false if all vectors are in R"? O None of the statements is false O alNot every orthogonal set in R" is linearly independent. O d)lf U is an n x n orthogonal matrix, then the rows of U form an orthogonal basis of R" O Statements a, b and c O b)lf y is a linear combination of non zero vectors from an orthogonal set, then the weights in the linear combination can be computed with row operations on a matrix O All the statements are false O c)The orthogonal projection of y onto v is the same as the orthogonal projection of y onto cv , where c is a non zero constant O Statements a, b and d O Statements b and c

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,...
Question
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Which of the following statements is (are) false if all vectors are in R"?
None of the statements is false
a)Not every orthogonal set in R" is linearly independent.
d)lf U is an n xn orthogonal matrix, then the rows of U form an orthogonal basis of R"
Statements a, b and c
O blf y is a linear combination of non zero vectors from an orthogonal set, then the weights in the linear combination can be computed with
row operations on a matrix
O All the statements are false
O c)The orthogonal projection of y onto v is the same as the orthogonal projection of y onto cv, where c is a non zero constant
O Statements a, b and d
O Statements b and c
Transcribed Image Text:Which of the following statements is (are) false if all vectors are in R"? None of the statements is false a)Not every orthogonal set in R" is linearly independent. d)lf U is an n xn orthogonal matrix, then the rows of U form an orthogonal basis of R" Statements a, b and c O blf y is a linear combination of non zero vectors from an orthogonal set, then the weights in the linear combination can be computed with row operations on a matrix O All the statements are false O c)The orthogonal projection of y onto v is the same as the orthogonal projection of y onto cv, where c is a non zero constant O Statements a, b and d O Statements b and c
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