Give a row-echelon form of the matrix A and give its rank: A = 24-2 -1 0 7 2 7 10 37 3
Give a row-echelon form of the matrix A and give its rank: A = 24-2 -1 0 7 2 7 10 37 3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![**Matrix Row-Echelon Form and Rank Explanation**
Given a matrix \( A \):
\[
A = \begin{bmatrix}
2 & 4 & -2 \\
-1 & 0 & 7 \\
2 & 7 & 10 \\
3 & 7 & 3
\end{bmatrix}
\]
**Objective:** Find the row-echelon form of the matrix \( A \) and determine its rank.
### Instructions:
To manipulate the matrix, you can resize it by clicking and dragging the bottom-right corner when applicable.
### Row-Echelon Form:
The row-echelon form of matrix \( A \) is:
\[
\begin{bmatrix}
0 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0
\end{bmatrix}
\]
### Rank:
The rank of matrix \( A \) is determined by the number of non-zero rows in its row-echelon form. Therefore:
\[
\text{Rank}(A) = 0
\]
This indicates that all rows have become zeros, implying the original matrix does not have any linearly independent rows.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7154a3f3-e619-45a8-a06e-684279d32bee%2F14106274-bca8-4685-bdcf-8c3b7cf49a84%2Foc62hab_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Matrix Row-Echelon Form and Rank Explanation**
Given a matrix \( A \):
\[
A = \begin{bmatrix}
2 & 4 & -2 \\
-1 & 0 & 7 \\
2 & 7 & 10 \\
3 & 7 & 3
\end{bmatrix}
\]
**Objective:** Find the row-echelon form of the matrix \( A \) and determine its rank.
### Instructions:
To manipulate the matrix, you can resize it by clicking and dragging the bottom-right corner when applicable.
### Row-Echelon Form:
The row-echelon form of matrix \( A \) is:
\[
\begin{bmatrix}
0 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & 0
\end{bmatrix}
\]
### Rank:
The rank of matrix \( A \) is determined by the number of non-zero rows in its row-echelon form. Therefore:
\[
\text{Rank}(A) = 0
\]
This indicates that all rows have become zeros, implying the original matrix does not have any linearly independent rows.
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