A = 2 - 4 4 -2 6-9 7 -3 -1 -10 18 -7
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.3: Matrix Approa To Solving Linear Systems
Problem 51PS
Related questions
Question
Find an LU factorization of matrix A.
L=
U=
![### Matrix Representation
In this section, we discuss the matrix \( A \) as presented in the image. A matrix is a rectangular array of numbers arranged in rows and columns.
Given Matrix \( A \):
\[
A = \begin{bmatrix}
2 & -4 & 4 & -2 \\
6 & -9 & 7 & -3 \\
-1 & -10 & 18 & -7 \\
\end{bmatrix}
\]
#### Structure
- The matrix \( A \) is a \( 3 \times 4 \) matrix, meaning it has 3 rows and 4 columns.
#### Elements of Matrix \( A \)
1. **First Row:**
- Element at (1,1): \( 2 \)
- Element at (1,2): \( -4 \)
- Element at (1,3): \( 4 \)
- Element at (1,4): \( -2 \)
2. **Second Row:**
- Element at (2,1): \( 6 \)
- Element at (2,2): \( -9 \)
- Element at (2,3): \( 7 \)
- Element at (2,4): \( -3 \)
3. **Third Row:**
- Element at (3,1): \( -1 \)
- Element at (3,2): \( -10 \)
- Element at (3,3): \( 18 \)
- Element at (3,4): \( -7 \)
Matrices are fundamental in various fields, including mathematics, computer science, physics, and engineering, due to their applicability in solving systems of linear equations, transformations, and more. Understanding matrices helps in performing operations such as addition, subtraction, multiplication, and determining inverses.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e11f595-a40a-4bf3-b7d2-0a0cab1f1556%2F7aa43fc9-e886-4966-bef7-eaee943033c0%2F069f4ls_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Matrix Representation
In this section, we discuss the matrix \( A \) as presented in the image. A matrix is a rectangular array of numbers arranged in rows and columns.
Given Matrix \( A \):
\[
A = \begin{bmatrix}
2 & -4 & 4 & -2 \\
6 & -9 & 7 & -3 \\
-1 & -10 & 18 & -7 \\
\end{bmatrix}
\]
#### Structure
- The matrix \( A \) is a \( 3 \times 4 \) matrix, meaning it has 3 rows and 4 columns.
#### Elements of Matrix \( A \)
1. **First Row:**
- Element at (1,1): \( 2 \)
- Element at (1,2): \( -4 \)
- Element at (1,3): \( 4 \)
- Element at (1,4): \( -2 \)
2. **Second Row:**
- Element at (2,1): \( 6 \)
- Element at (2,2): \( -9 \)
- Element at (2,3): \( 7 \)
- Element at (2,4): \( -3 \)
3. **Third Row:**
- Element at (3,1): \( -1 \)
- Element at (3,2): \( -10 \)
- Element at (3,3): \( 18 \)
- Element at (3,4): \( -7 \)
Matrices are fundamental in various fields, including mathematics, computer science, physics, and engineering, due to their applicability in solving systems of linear equations, transformations, and more. Understanding matrices helps in performing operations such as addition, subtraction, multiplication, and determining inverses.
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