Assume that A is row equivalent to B. Find bases for Nul A, Col A, and Row A. 12 5-7 6 1 2 0 3 6 4 8 -2 16 7 3 6 0 97 B= 120 3 5 005 10 5 000 0 -7 000 0 1 A column vector basis for Nul A is (Use a comma to separate vectors as needed.) O X
Assume that A is row equivalent to B. Find bases for Nul A, Col A, and Row A. 12 5-7 6 1 2 0 3 6 4 8 -2 16 7 3 6 0 97 B= 120 3 5 005 10 5 000 0 -7 000 0 1 A column vector basis for Nul A is (Use a comma to separate vectors as needed.) O X
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,...
Related questions
Question
![**Problem Statement:**
Assume that matrix \( A \) is row equivalent to matrix \( B \). Find bases for the null space (Nul \( A \)), column space (Col \( A \)), and row space (Row \( A \)).
**Matrices:**
\[ A = \begin{bmatrix} 1 & 2 & 5 & -7 & 6 \\ 1 & 2 & 0 & 3 & 6 \\ 4 & 8 & -2 & 16 & 7 \\ 3 & 6 & 0 & 9 & 7 \end{bmatrix} \]
\[ B = \begin{bmatrix} 1 & 2 & 0 & 3 & 5 \\ 0 & 0 & 5 & -10 & 5 \\ 0 & 0 & 0 & 0 & -7 \\ 0 & 0 & 0 & 0 & 0 \end{bmatrix} \]
**Instructions:**
- Find a column vector basis for the null space of matrix \( A \).
- Use a comma to separate vectors as needed.
**Explanation of Matrices:**
Matrix \( A \) is a 4x5 matrix, and matrix \( B \) is in row echelon form equivalent to \( A \). The goal is to determine bases for the null space, column space, and row space by analyzing the row echelon form matrix \( B \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95f0b7f6-52d2-4b69-91d7-019b1ba2e2f5%2F68c263a1-904c-49ff-86e3-c736a3010630%2Fj2jy82f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Assume that matrix \( A \) is row equivalent to matrix \( B \). Find bases for the null space (Nul \( A \)), column space (Col \( A \)), and row space (Row \( A \)).
**Matrices:**
\[ A = \begin{bmatrix} 1 & 2 & 5 & -7 & 6 \\ 1 & 2 & 0 & 3 & 6 \\ 4 & 8 & -2 & 16 & 7 \\ 3 & 6 & 0 & 9 & 7 \end{bmatrix} \]
\[ B = \begin{bmatrix} 1 & 2 & 0 & 3 & 5 \\ 0 & 0 & 5 & -10 & 5 \\ 0 & 0 & 0 & 0 & -7 \\ 0 & 0 & 0 & 0 & 0 \end{bmatrix} \]
**Instructions:**
- Find a column vector basis for the null space of matrix \( A \).
- Use a comma to separate vectors as needed.
**Explanation of Matrices:**
Matrix \( A \) is a 4x5 matrix, and matrix \( B \) is in row echelon form equivalent to \( A \). The goal is to determine bases for the null space, column space, and row space by analyzing the row echelon form matrix \( B \).
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 5 steps with 5 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education