File Preview A = 000 400 0000 06 020000 100 000 00 3000 50 00005 (a) Using any method, calculate the determinant of A. det(A)
File Preview A = 000 400 0000 06 020000 100 000 00 3000 50 00005 (a) Using any method, calculate the determinant of A. det(A)
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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please answer the screenshort
please also Calculate the inverse of A
and calculate the adjugate of A.
![Here is the transcribed content from the image, which is designed for an educational website:
---
**Matrix Determinant Calculation**
Consider the matrix \( A \) given below:
\[
A =
\begin{bmatrix}
0 & 0 & 0 & 4 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 6 \\
0 & 2 & 0 & 0 & 0 & 0 \\
1 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 3 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 5 & 0 \\
\end{bmatrix}
\]
(a) Using any method, calculate the determinant of \( A \), denoted as \(\det(A)\).
---
The matrix \( A \) is a \( 6 \times 6 \) matrix. Calculating the determinant of this matrix can be done using various methods, such as cofactor expansion or leveraging properties of triangular matrices if applicable. In this particular example, note the presence of zeros which might simplify the calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2903bb2a-771d-40b7-a62d-703de2e08baa%2F60a4d39d-ac10-4fce-a222-1ce5ad6cabce%2Fhqi9rhi_processed.png&w=3840&q=75)
Transcribed Image Text:Here is the transcribed content from the image, which is designed for an educational website:
---
**Matrix Determinant Calculation**
Consider the matrix \( A \) given below:
\[
A =
\begin{bmatrix}
0 & 0 & 0 & 4 & 0 & 0 \\
0 & 0 & 0 & 0 & 0 & 6 \\
0 & 2 & 0 & 0 & 0 & 0 \\
1 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 3 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 & 5 & 0 \\
\end{bmatrix}
\]
(a) Using any method, calculate the determinant of \( A \), denoted as \(\det(A)\).
---
The matrix \( A \) is a \( 6 \times 6 \) matrix. Calculating the determinant of this matrix can be done using various methods, such as cofactor expansion or leveraging properties of triangular matrices if applicable. In this particular example, note the presence of zeros which might simplify the calculations.
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