Consider the matrix B 1 is given by where A₁ = A₂ = - 1114 -5 -5 3-1 1 3 3 2 -3 3 5 -4 det (A₁) + 22 Then det (B) using the cofactor expansion along column det (A₂)+ det(A3)+ 4 det (A4)
Consider the matrix B 1 is given by where A₁ = A₂ = - 1114 -5 -5 3-1 1 3 3 2 -3 3 5 -4 det (A₁) + 22 Then det (B) using the cofactor expansion along column det (A₂)+ det(A3)+ 4 det (A4)
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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See image below and A3 and A4 not shown in image is also a 3 *3 matrix
![Consider the matrix \( B = \begin{bmatrix} 1 & 1 & 1 & 4 \\ -5 & -5 & 3 & -1 \\ 1 & 3 & 3 & 2 \\ -3 & 3 & 5 & -4 \end{bmatrix} \). Then, \(\det(B)\) using the cofactor expansion along column 1 is given by
\[ \boxed{} \, \det(A_1) + \boxed{} \, \det(A_2) + \boxed{} \, \det(A_3) + \boxed{} \, \det(A_4) \]
where
\[ A_1 = \begin{bmatrix} \boxed{} & \boxed{} & \boxed{} \\ \boxed{} & \boxed{} & \boxed{} \\ \boxed{} & \boxed{} & \boxed{} \end{bmatrix} \]
\[ A_2 = \begin{bmatrix} \boxed{} & \boxed{} & \boxed{} \\ \boxed{} & \boxed{} & \boxed{} \\ \boxed{} & \boxed{} & \boxed{} \end{bmatrix} \]
The matrices \( A_3 \) and \( A_4 \) are similarly structured with blank spaces for their elements.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F181283bb-83dc-4f09-86f1-fac04e6d4723%2F82b7d94f-5ad9-406c-900b-bb46c3396bed%2Fgrte8fu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the matrix \( B = \begin{bmatrix} 1 & 1 & 1 & 4 \\ -5 & -5 & 3 & -1 \\ 1 & 3 & 3 & 2 \\ -3 & 3 & 5 & -4 \end{bmatrix} \). Then, \(\det(B)\) using the cofactor expansion along column 1 is given by
\[ \boxed{} \, \det(A_1) + \boxed{} \, \det(A_2) + \boxed{} \, \det(A_3) + \boxed{} \, \det(A_4) \]
where
\[ A_1 = \begin{bmatrix} \boxed{} & \boxed{} & \boxed{} \\ \boxed{} & \boxed{} & \boxed{} \\ \boxed{} & \boxed{} & \boxed{} \end{bmatrix} \]
\[ A_2 = \begin{bmatrix} \boxed{} & \boxed{} & \boxed{} \\ \boxed{} & \boxed{} & \boxed{} \\ \boxed{} & \boxed{} & \boxed{} \end{bmatrix} \]
The matrices \( A_3 \) and \( A_4 \) are similarly structured with blank spaces for their elements.
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