20 2 Compute det B° where B = 2 2 4 1 2 2 det B5 (Simplify your answer.)
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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![**Task: Calculate the Determinant of a Matrix Raised to a Power**
The problem provided is to compute the determinant of the fifth power of matrix \( \mathbf{B} \) given as:
\[ \mathbf{B} = \begin{bmatrix} 2 & 0 & 2 \\ 2 & 2 & 4 \\ 1 & 2 & 2 \end{bmatrix} \]
The goal is to find \( \det(\mathbf{B}^5) \).
**Solution Steps:**
1. First, calculate \( \det(\mathbf{B}) \).
2. Raise the determinant to the fifth power: \( \det(\mathbf{B}^5) = (\det(\mathbf{B}))^5 \).
Please simplify your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17636a1f-5478-4a39-bbde-caed22af3378%2F419b8d5a-9b00-4a9c-b74c-684b347e8734%2Ffdher1_processed.png&w=3840&q=75)
Transcribed Image Text:**Task: Calculate the Determinant of a Matrix Raised to a Power**
The problem provided is to compute the determinant of the fifth power of matrix \( \mathbf{B} \) given as:
\[ \mathbf{B} = \begin{bmatrix} 2 & 0 & 2 \\ 2 & 2 & 4 \\ 1 & 2 & 2 \end{bmatrix} \]
The goal is to find \( \det(\mathbf{B}^5) \).
**Solution Steps:**
1. First, calculate \( \det(\mathbf{B}) \).
2. Raise the determinant to the fifth power: \( \det(\mathbf{B}^5) = (\det(\mathbf{B}))^5 \).
Please simplify your answer.
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