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If A is a 8 x 8 matrix and det(A) = 2, compute det(-.

If A is a 8 x 8 matrix and det(A) = 2, compute det(-.

Advanced Engineering Mathematics
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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Hello can you please do this the matrices way step by step I have provided the answer and question 

### Problem 8.1 If \( A \) is an 8 \(\times\) 8 matrix and \(\det(A) = 2\), compute \(\det(-A)\). Explanation: Consider matrix \( A \) and its determinant. The determinant of the matrix \( -A \) can be found by taking the determinant of \( A \) and multiplying it by \((-1)\) raised to the power of the size of the matrix. Since \( A \) is an 8 \(\times\) 8 matrix, the size is 8. Thus, \[\det(-A) = (-1)^8 \times \det(A) = 1 \times 2 = 2\]. Therefore, \(\det(-A) = 2\).
Transcribed Image Text:### Problem 8.1 If \( A \) is an 8 \(\times\) 8 matrix and \(\det(A) = 2\), compute \(\det(-A)\). Explanation: Consider matrix \( A \) and its determinant. The determinant of the matrix \( -A \) can be found by taking the determinant of \( A \) and multiplying it by \((-1)\) raised to the power of the size of the matrix. Since \( A \) is an 8 \(\times\) 8 matrix, the size is 8. Thus, \[\det(-A) = (-1)^8 \times \det(A) = 1 \times 2 = 2\]. Therefore, \(\det(-A) = 2\).
The text in the image reads "8.1 2." There are no graphs or diagrams present in the image. It appears to be a simple numeric or alphanumeric notation which could be a part of a list or a section marker from a book, document, or educational material.
Transcribed Image Text:The text in the image reads "8.1 2." There are no graphs or diagrams present in the image. It appears to be a simple numeric or alphanumeric notation which could be a part of a list or a section marker from a book, document, or educational material.
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