Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
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.](https://content.bartleby.com/qna-images/question/6e11f595-a40a-4bf3-b7d2-0a0cab1f1556/7aa43fc9-e886-4966-bef7-eaee943033c0/069f4ls_processed.jpeg)
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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution
Trending nowThis is a popular solution!
Step by stepSolved in 2 steps with 1 images
Knowledge Booster
Similar questions
- Find a 3 x 2 matrix A and has LU factorization where L is diagonal. A =arrow_forwardFind the matrices in the factorization A = PTLU, where matrix A= [(1,6,0),(2,1,0),(0,2,1)]arrow_forwardSolve the following equation involving a determinant. If you have multiple answers, enter them as a list, separated by commas. 1 det( 2 = 38 x + 3 X =arrow_forward
Recommended textbooks for you
- Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
Numerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill Education
Introductory Mathematics for Engineering Applicat...Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEY 
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
Advanced Engineering Mathematics
Advanced Math
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:9780073397924
Author:Steven C. Chapra Dr., Raymond P. Canale
Publisher:McGraw-Hill Education
Introductory Mathematics for Engineering Applicat...
Advanced Math
ISBN:9781118141809
Author:Nathan Klingbeil
Publisher:WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,