2 -1 4 a) 1 3 -1 2 1 11 (b) 1 -2 5 002 2 2 1 -6 7 5 4 -4 -2 -1
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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4. Find the determinants by row reduction to echelon form.
![### Matrices for Vector Spaces
Here we will examine two matrices, labeled (a) and (b). These matrices can be used to illustrate various concepts in linear algebra, such as matrix operations, determinants, eigenvalues, and systems of linear equations.
#### Matrix (a)
\[
\begin{pmatrix}
2 & -1 & 4 \\
1 & 3 & -1 \\
2 & 1 & 11
\end{pmatrix}
\]
**Description:**
Matrix (a) is a 3x3 matrix with the following elements:
- First row: (2, -1, 4)
- Second row: (1, 3, -1)
- Third row: (2, 1, 11)
#### Matrix (b)
\[
\begin{pmatrix}
1 & -2 & 5 & 2 \\
0 & 0 & 2 & 1 \\
2 & -6 & 7 & 5 \\
-1 & 4 & -4 & -2
\end{pmatrix}
\]
**Description:**
Matrix (b) is a 4x4 matrix with the following elements:
- First row: (1, -2, 5, 2)
- Second row: (0, 0, 2, 1)
- Third row: (2, -6, 7, 5)
- Fourth row: (-1, 4, -4, -2)
**Explanation:**
Both of these matrices serve as excellent examples for exploring operations like matrix multiplication, row reduction, and calculation of determinants. We will use these specific matrices to demonstrate and practice these mathematical procedures.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8d07e113-70c7-44ea-a54a-4dad627b44c8%2F4c5fc92d-67e7-44ca-bba9-9ee052bbe733%2Flu37fz3_processed.png&w=3840&q=75)
Transcribed Image Text:### Matrices for Vector Spaces
Here we will examine two matrices, labeled (a) and (b). These matrices can be used to illustrate various concepts in linear algebra, such as matrix operations, determinants, eigenvalues, and systems of linear equations.
#### Matrix (a)
\[
\begin{pmatrix}
2 & -1 & 4 \\
1 & 3 & -1 \\
2 & 1 & 11
\end{pmatrix}
\]
**Description:**
Matrix (a) is a 3x3 matrix with the following elements:
- First row: (2, -1, 4)
- Second row: (1, 3, -1)
- Third row: (2, 1, 11)
#### Matrix (b)
\[
\begin{pmatrix}
1 & -2 & 5 & 2 \\
0 & 0 & 2 & 1 \\
2 & -6 & 7 & 5 \\
-1 & 4 & -4 & -2
\end{pmatrix}
\]
**Description:**
Matrix (b) is a 4x4 matrix with the following elements:
- First row: (1, -2, 5, 2)
- Second row: (0, 0, 2, 1)
- Third row: (2, -6, 7, 5)
- Fourth row: (-1, 4, -4, -2)
**Explanation:**
Both of these matrices serve as excellent examples for exploring operations like matrix multiplication, row reduction, and calculation of determinants. We will use these specific matrices to demonstrate and practice these mathematical procedures.
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