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20. Let {u1, uz) be the orthonormal basis obtained by applying the Gram-Schmidt procedure to the basis {1, 12} of Then uz is equal to R2, where r = and r2 = (a) ) (6) (3) () (b) (c) (d) (e) None of the above 21. Which of the following is the equation of the plane passing through the point (2,3, 4) and normal to (a) y -=2 (b) := 4 (c) -z+ 2y + 5: = 0 (d) -z - y = 1 (e) None of the above 22. Which of the following statements about an n x n matrix A is NOT ALWAYS TRUE? (a) A is invertible if and only if its rows span R* (b) The equation Ar = 0 has only the trivial solution if and only if A is invertible (c) A is diagonalizable if and only if it hasn distinct eigenvalues (d) The rank of A is equal to the rank of its reduced row echelon form (e) None of the above these statements are always true

20. Let {u1, uz) be the orthonormal basis obtained by applying the Gram-Schmidt procedure to the basis {1, 12} of Then uz is equal to R2, where r = and r2 = (a) ) (6) (3) () (b) (c) (d) (e) None of the above 21. Which of the following is the equation of the plane passing through the point (2,3, 4) and normal to (a) y -=2 (b) := 4 (c) -z+ 2y + 5: = 0 (d) -z - y = 1 (e) None of the above 22. Which of the following statements about an n x n matrix A is NOT ALWAYS TRUE? (a) A is invertible if and only if its rows span R* (b) The equation Ar = 0 has only the trivial solution if and only if A is invertible (c) A is diagonalizable if and only if it hasn distinct eigenvalues (d) The rank of A is equal to the rank of its reduced row echelon form (e) None of the above these statements are always true

Algebra and Trigonometry (6th Edition)
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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20. Let {u1, uz) be the orthonormal basis obtained by applying the Gram-Schmidt procedure to the basis {1, 12} of Then uz is equal to R2, where r = and r2 = (a) ) (6) (3) () (b) (c) (d) (e) None of the above 21. Which of the following is the equation of the plane passing through the point (2,3, 4) and normal to (a) y -=2 (b) := 4 (c) -z+ 2y + 5: = 0 (d) -z - y = 1 (e) None of the above 22. Which of the following statements about an n x n matrix A is NOT ALWAYS TRUE? (a) A is invertible if and only if its rows span R* (b) The equation Ar = 0 has only the trivial solution if and only if A is invertible (c) A is diagonalizable if and only if it hasn distinct eigenvalues (d) The rank of A is equal to the rank of its reduced row echelon form (e) None of the above these statements are always true
Transcribed Image Text:20. Let {u1, uz) be the orthonormal basis obtained by applying the Gram-Schmidt procedure to the basis {1, 12} of Then uz is equal to R2, where r = and r2 = (a) ) (6) (3) () (b) (c) (d) (e) None of the above 21. Which of the following is the equation of the plane passing through the point (2,3, 4) and normal to (a) y -=2 (b) := 4 (c) -z+ 2y + 5: = 0 (d) -z - y = 1 (e) None of the above 22. Which of the following statements about an n x n matrix A is NOT ALWAYS TRUE? (a) A is invertible if and only if its rows span R* (b) The equation Ar = 0 has only the trivial solution if and only if A is invertible (c) A is diagonalizable if and only if it hasn distinct eigenvalues (d) The rank of A is equal to the rank of its reduced row echelon form (e) None of the above these statements are always true
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