Let A = 1 - 4 2 -2 - 1 4 0 0 2 b₁ and b = b₂ Show that the equation Ax=b does not have a solution for all possible b b3 and describe the set of all b for which Ax=b does have a solution.
Let A = 1 - 4 2 -2 - 1 4 0 0 2 b₁ and b = b₂ Show that the equation Ax=b does not have a solution for all possible b b3 and describe the set of all b for which Ax=b does have a solution.
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 71E
Related questions
Question
100%
![1 -2 - 1
4-8
- 4
2 0 2
and describe the set of all b for which Ax=b does have a solution.
Let A =
b₁
0 and b = b₂ Show that the equation Ax=b does not have a solution for all possible b
b3
How can it be shown that the equation Ax=b does not have a solution for all possible b? Choose the correct answer
below.
O A. Row reduce the augmented matrix [ A b] to demonstrate that [ A b] has a pivot position in every row.
B. Row reduce the matrix A to demonstrate that A does not have a pivot position in every row.
C. Row reduce the matrix A to demonstrate that A has a pivot position in every row.
D. Find a vector x for which Ax=b is the zero vector.
O E. Find a vector b for which the solution to Ax=b is the zero vector.
Describe the set of all b for which Ax=b does have a solution.
0 = 2b₁ +2b₂ + b3
(Type an expression using b₁,b₂, and b3 as the variables and 1 as the coefficient of b3.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8109dbb5-39b2-442d-b17d-793e299fca4a%2F4246d080-eaf5-4e2c-a008-c8f4df282428%2F69dvq3b_processed.png&w=3840&q=75)
Transcribed Image Text:1 -2 - 1
4-8
- 4
2 0 2
and describe the set of all b for which Ax=b does have a solution.
Let A =
b₁
0 and b = b₂ Show that the equation Ax=b does not have a solution for all possible b
b3
How can it be shown that the equation Ax=b does not have a solution for all possible b? Choose the correct answer
below.
O A. Row reduce the augmented matrix [ A b] to demonstrate that [ A b] has a pivot position in every row.
B. Row reduce the matrix A to demonstrate that A does not have a pivot position in every row.
C. Row reduce the matrix A to demonstrate that A has a pivot position in every row.
D. Find a vector x for which Ax=b is the zero vector.
O E. Find a vector b for which the solution to Ax=b is the zero vector.
Describe the set of all b for which Ax=b does have a solution.
0 = 2b₁ +2b₂ + b3
(Type an expression using b₁,b₂, and b3 as the variables and 1 as the coefficient of b3.)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 6 steps with 6 images
Recommended textbooks for you
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning