In A & B, evaluate the determinant of the given matrix by inspection.
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
In A & B, evaluate the determinant of the given matrix by inspection.
![This image depicts a 4x4 matrix, which is a key concept in linear algebra. The matrix is presented in a standard rectangular array of numbers, arranged in rows and columns. Here is the matrix:
\[
\begin{pmatrix}
0 & 0 & 0 & 0 \\
1 & 2 & 0 & 0 \\
0 & 4 & 3 & 0 \\
1 & 2 & 3 & 8
\end{pmatrix}
\]
Each element of the matrix is a number arranged in a specific row and column. This particular matrix consists of the following elements:
- Element in the first row and first column is 0.
- Element in the first row and second column is 0.
- Element in the first row and third column is 0.
- Element in the first row and fourth column is 0.
- Element in the second row and first column is 1.
- Element in the second row and second column is 2.
- Element in the second row and third column is 0.
- Element in the second row and fourth column is 0.
- Element in the third row and first column is 0.
- Element in the third row and second column is 4.
- Element in the third row and third column is 3.
- Element in the third row and fourth column is 0.
- Element in the fourth row and first column is 1.
- Element in the fourth row and second column is 2.
- Element in the fourth row and third column is 3.
- Element in the fourth row and fourth column is 8.
Matrices are used in various mathematical and engineering disciplines to represent linear transformations, solve systems of linear equations, and many other applications. Understanding the structure and properties of matrices is fundamental in these areas.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87643561-f7f8-47c3-82b0-7735ae0706bf%2F43cb570d-2046-440b-b54a-50bad1aa7485%2F6k4n3co_processed.png&w=3840&q=75)
Transcribed Image Text:This image depicts a 4x4 matrix, which is a key concept in linear algebra. The matrix is presented in a standard rectangular array of numbers, arranged in rows and columns. Here is the matrix:
\[
\begin{pmatrix}
0 & 0 & 0 & 0 \\
1 & 2 & 0 & 0 \\
0 & 4 & 3 & 0 \\
1 & 2 & 3 & 8
\end{pmatrix}
\]
Each element of the matrix is a number arranged in a specific row and column. This particular matrix consists of the following elements:
- Element in the first row and first column is 0.
- Element in the first row and second column is 0.
- Element in the first row and third column is 0.
- Element in the first row and fourth column is 0.
- Element in the second row and first column is 1.
- Element in the second row and second column is 2.
- Element in the second row and third column is 0.
- Element in the second row and fourth column is 0.
- Element in the third row and first column is 0.
- Element in the third row and second column is 4.
- Element in the third row and third column is 3.
- Element in the third row and fourth column is 0.
- Element in the fourth row and first column is 1.
- Element in the fourth row and second column is 2.
- Element in the fourth row and third column is 3.
- Element in the fourth row and fourth column is 8.
Matrices are used in various mathematical and engineering disciplines to represent linear transformations, solve systems of linear equations, and many other applications. Understanding the structure and properties of matrices is fundamental in these areas.
![Here is our given matrix, represented in a standard 3x3 format.
\[
\begin{bmatrix}
2 & 0 & 0 \\
0 & 2 & 0 \\
0 & 0 & 2
\end{bmatrix}
\]
This is a diagonal matrix where all the diagonal elements are equal to 2 and all non-diagonal elements are zero. Diagonal matrices are a special type of square matrix with the property that all off-diagonal elements are zero.
In this specific matrix:
- The element in the first row and first column (position [1,1]) is 2.
- The element in the second row and second column (position [2,2]) is 2.
- The element in the third row and third column (position [3,3]) is 2.
All other elements are 0.
This matrix is often used in linear transformations and can represent scaling in 3D space where each axis is scaled by the factor of 2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87643561-f7f8-47c3-82b0-7735ae0706bf%2F43cb570d-2046-440b-b54a-50bad1aa7485%2Ffy1xyd_processed.png&w=3840&q=75)
Transcribed Image Text:Here is our given matrix, represented in a standard 3x3 format.
\[
\begin{bmatrix}
2 & 0 & 0 \\
0 & 2 & 0 \\
0 & 0 & 2
\end{bmatrix}
\]
This is a diagonal matrix where all the diagonal elements are equal to 2 and all non-diagonal elements are zero. Diagonal matrices are a special type of square matrix with the property that all off-diagonal elements are zero.
In this specific matrix:
- The element in the first row and first column (position [1,1]) is 2.
- The element in the second row and second column (position [2,2]) is 2.
- The element in the third row and third column (position [3,3]) is 2.
All other elements are 0.
This matrix is often used in linear transformations and can represent scaling in 3D space where each axis is scaled by the factor of 2.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Recommended textbooks for you
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
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,
