If A is a 8 x 8 matrix and det(A) = 2, compute det(-.
Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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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, \(\det(-A) = 2\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F460d6b43-992c-4555-b09d-3f6791ba763b%2F9e567cb3-cf61-46f4-9e17-6dc0679c6264%2Fin7m61a_processed.jpeg&w=3840&q=75)
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, \(\det(-A) = 2\).
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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