What is the rank of the matrix A = 2 1 5 -1 2 -5 0 3? -3

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,...
icon
Related questions
Question
**Question:**

What is the rank of the matrix \( A = \begin{bmatrix} 2 & -1 & 0 \\ 1 & 2 & 3 \\ 5 & -5 & -3 \end{bmatrix} \)? 

**Explanation:**

To find the rank of a matrix, we determine the number of linearly independent rows (or columns). Here's a step-by-step guide to finding the rank of this matrix:

1. **Row Reduction:** Convert the matrix into row-echelon form using elementary row operations.
2. **Identify Non-Zero Rows:** Count the number of non-zero rows in the row-echelon form.
3. **Rank:** The rank of the matrix is equal to the number of non-zero rows.

By following these steps, we can find the rank of the matrix \( A \).
Transcribed Image Text:**Question:** What is the rank of the matrix \( A = \begin{bmatrix} 2 & -1 & 0 \\ 1 & 2 & 3 \\ 5 & -5 & -3 \end{bmatrix} \)? **Explanation:** To find the rank of a matrix, we determine the number of linearly independent rows (or columns). Here's a step-by-step guide to finding the rank of this matrix: 1. **Row Reduction:** Convert the matrix into row-echelon form using elementary row operations. 2. **Identify Non-Zero Rows:** Count the number of non-zero rows in the row-echelon form. 3. **Rank:** The rank of the matrix is equal to the number of non-zero rows. By following these steps, we can find the rank of the matrix \( A \).
Expert Solution
Step 1

See this solution in below. 

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education