Suppose A is a 5 by 5 matrix and the reduced echelon form of A is U. Decide whether each of the following statements is true. Statement 1: A and U must have the same rank. Statement 2: If v is an eigenvector of A with eigenvalue 0 then v must also be an eigenvector of U with eigenvalue 0. Select one alternative Statement 1 is false and statement 2 is true Statement 1 is false and statement 2 is false Statement 1 is true and statement 2 is true Statement 1 is true and statement 2 is false
Suppose A is a 5 by 5 matrix and the reduced echelon form of A is U. Decide whether each of the following statements is true. Statement 1: A and U must have the same rank. Statement 2: If v is an eigenvector of A with eigenvalue 0 then v must also be an eigenvector of U with eigenvalue 0. Select one alternative Statement 1 is false and statement 2 is true Statement 1 is false and statement 2 is false Statement 1 is true and statement 2 is true Statement 1 is true and statement 2 is false
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 34E
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![Suppose A is a 5 by 5 matrix and the reduced echelon form of A is U.
Decide whether each of the following statements is true.
Statement 1:
A and U must have the same rank.
Statement 2:
If v is an eigenvector of A with eigenvalue 0 then v must also be an eigenvector of U with eigenvalue 0.
Select one alternative
© Statement 1 is false and statement 2 is true
Statement 1 is false and statement 2 is false
O Statement 1 is true and statement 2 is true
Statement 1 is true and statement 2 is false
O](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0b6e0f90-4242-44aa-a3fd-f315669bac72%2F1489e89c-b17f-49f5-8619-410f6d3b84e7%2Fo79l7i_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose A is a 5 by 5 matrix and the reduced echelon form of A is U.
Decide whether each of the following statements is true.
Statement 1:
A and U must have the same rank.
Statement 2:
If v is an eigenvector of A with eigenvalue 0 then v must also be an eigenvector of U with eigenvalue 0.
Select one alternative
© Statement 1 is false and statement 2 is true
Statement 1 is false and statement 2 is false
O Statement 1 is true and statement 2 is true
Statement 1 is true and statement 2 is false
O
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