1 2 0 0 -5 0 0 1 0 -4 0 0 0 1 2 Lo 0 0 0 0J
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Find a basis for null space of the matrix
![The image shows a matrix that can be used in linear algebra and various mathematical computations. The matrix is a \(4 \times 5\) matrix, which is an augmented matrix often used in solving systems of linear equations. Here is the matrix transcribed:
\[
\begin{bmatrix}
1 & 2 & 0 & 0 & -5 \\
0 & 0 & 1 & 0 & -4 \\
0 & 0 & 0 & 1 & 2 \\
0 & 0 & 0 & 0 & 0 \\
\end{bmatrix}
\]
**Matrix Explanation:**
- **Rows and Columns:** The matrix consists of four rows and five columns.
- **Element Explanation:**
- The first row has elements: 1, 2, 0, 0, -5.
- The second row has elements: 0, 0, 1, 0, -4.
- The third row has elements: 0, 0, 0, 1, 2.
- The fourth row consists of all zeros.
- **Usage:** Such matrices are typically utilized in row reduction methods (like Gaussian elimination) to solve linear systems. The final column may represent the constants from equations resulting from a linear system.
This matrix can help illustrate concepts such as row reduction and solution analysis in linear algebra.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9f624280-ac22-40d0-83d1-40fb95ff1322%2F25306873-f738-45a4-94f4-834ce2e68167%2Fj15b02s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image shows a matrix that can be used in linear algebra and various mathematical computations. The matrix is a \(4 \times 5\) matrix, which is an augmented matrix often used in solving systems of linear equations. Here is the matrix transcribed:
\[
\begin{bmatrix}
1 & 2 & 0 & 0 & -5 \\
0 & 0 & 1 & 0 & -4 \\
0 & 0 & 0 & 1 & 2 \\
0 & 0 & 0 & 0 & 0 \\
\end{bmatrix}
\]
**Matrix Explanation:**
- **Rows and Columns:** The matrix consists of four rows and five columns.
- **Element Explanation:**
- The first row has elements: 1, 2, 0, 0, -5.
- The second row has elements: 0, 0, 1, 0, -4.
- The third row has elements: 0, 0, 0, 1, 2.
- The fourth row consists of all zeros.
- **Usage:** Such matrices are typically utilized in row reduction methods (like Gaussian elimination) to solve linear systems. The final column may represent the constants from equations resulting from a linear system.
This matrix can help illustrate concepts such as row reduction and solution analysis in linear algebra.
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