Use the fact that matrices A and B are row-equivalent. A = −2 −5 8 0 −17 1 3 −5 1 5 −1 1 −3 7 −33 1 7 −13 5 −3 B = 1 0 1 0 1 0 1 −2 0 3 0 0 0 1 −5 0 0 0 0 0 (a) Find the rank and nullity of A.
Use the fact that matrices A and B are row-equivalent. A = −2 −5 8 0 −17 1 3 −5 1 5 −1 1 −3 7 −33 1 7 −13 5 −3 B = 1 0 1 0 1 0 1 −2 0 3 0 0 0 1 −5 0 0 0 0 0 (a) Find the rank and nullity of A.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section: Chapter Questions
Problem 17RQ
Related questions
Question
Use the fact that matrices A and B are row-equivalent.
A =
|
−2 | −5 | 8 | 0 | −17 |
|
||
1 | 3 | −5 | 1 | 5 | ||||
−1 | 1 | −3 | 7 | −33 | ||||
1 | 7 | −13 | 5 | −3 |
B =
|
1 | 0 | 1 | 0 | 1 |
|
||
0 | 1 | −2 | 0 | 3 | ||||
0 | 0 | 0 | 1 | −5 | ||||
0 | 0 | 0 | 0 | 0 |
(a) Find the rank and nullity of A.
(d) Find a basis for the column space of A.
(e) Determine whether or not the rows of A are linearly independent.
(f) Let the columns of A be denoted by a1, a2, a3, a4, and a5. Which of the following sets is (are) linearly independent? (Select all that apply.)
rank | |
nullity |
(d) Find a basis for the column space of A.
|
|
|
(e) Determine whether or not the rows of A are linearly independent.
independentdependent
(f) Let the columns of A be denoted by a1, a2, a3, a4, and a5. Which of the following sets is (are) linearly independent? (Select all that apply.)
{a1, a2, a4}{a1, a2, a3}{a1, a3, a5}
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning