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20 2 ompute det B° where B = 1 1 4 1 3 1 et B° = (Simplify your answer.)

20 2 ompute det B° where B = 1 1 4 1 3 1 et B° = (Simplify your answer.)

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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**Compute \(\det \mathbf{B}^3\) where \(\mathbf{B} = \begin{bmatrix} 2 & 0 & 2 \\ 1 & 1 & 4 \\ 1 & 3 & 1 \end{bmatrix}\).** **\(\det \mathbf{B}^3 = \_\_\) (Simplify your answer.)** This exercise involves finding the determinant of the matrix \(\mathbf{B}\) and using it to compute \(\det \mathbf{B}^3\). ### Matrix Details: - \(\mathbf{B}\) is a 3x3 matrix: - First row: \([2, 0, 2]\) - Second row: \([1, 1, 4]\) - Third row: \([1, 3, 1]\) To solve this, find the determinant of \(\mathbf{B}\) and use the property of determinants: \(\det(\mathbf{B}^n) = (\det \mathbf{B})^n\).
Transcribed Image Text:**Compute \(\det \mathbf{B}^3\) where \(\mathbf{B} = \begin{bmatrix} 2 & 0 & 2 \\ 1 & 1 & 4 \\ 1 & 3 & 1 \end{bmatrix}\).** **\(\det \mathbf{B}^3 = \_\_\) (Simplify your answer.)** This exercise involves finding the determinant of the matrix \(\mathbf{B}\) and using it to compute \(\det \mathbf{B}^3\). ### Matrix Details: - \(\mathbf{B}\) is a 3x3 matrix: - First row: \([2, 0, 2]\) - Second row: \([1, 1, 4]\) - Third row: \([1, 3, 1]\) To solve this, find the determinant of \(\mathbf{B}\) and use the property of determinants: \(\det(\mathbf{B}^n) = (\det \mathbf{B})^n\).
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