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

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

Algebra and Trigonometry (6th Edition)
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,...
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**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 \( A \).
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