Compute the determinant by cofactor expansion. At each step, choose a row or column that involves the least amount of computation. 2 0 -4 O 8 -7 3 9 -7 2 O 0 1 005 = (Simplify your answer.) 2 O 0 O 8 -7 3 9 -7 1 2 -4 0 LO 00 5
Compute the determinant by cofactor expansion. At each step, choose a row or column that involves the least amount of computation. 2 0 -4 O 8 -7 3 9 -7 2 O 0 1 005 = (Simplify your answer.) 2 O 0 O 8 -7 3 9 -7 1 2 -4 0 LO 00 5
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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![**How to Compute the Determinant by Cofactor Expansion**
When computing the determinant, choose a row or column that minimizes computation:
### 4x4 Matrix:
\[
\begin{vmatrix}
2 & 8 & -7 & 3 \\
0 & -4 & 9 & -7 \\
0 & 0 & 1 & 2 \\
0 & 0 & 0 & 5 \\
\end{vmatrix}
\]
### Explanation:
This is a 4x4 matrix. To optimize calculation, consider expanding across the last row or column, as it contains zeros which simplify the process.
In this context, the determinant of the matrix is structured as follows (before simplification):
\[
= \begin{vmatrix}
2 & 8 & -7 & 3 \\
0 & -4 & 9 & -7 \\
0 & 0 & 1 & 2 \\
0 & 0 & 0 & 5 \\
\end{vmatrix}
\]
#### Answer Box:
Provide your simplified answer:
__[ ]__ *(Simplify your answer.)*
This exercise illustrates the importance of selecting strategic rows or columns to minimize calculations during cofactor expansion.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe00cebfb-aec4-474d-8979-79a2d105b819%2F272b518a-640f-4ef9-8d69-117214e80163%2Ft78z2o_processed.png&w=3840&q=75)
Transcribed Image Text:**How to Compute the Determinant by Cofactor Expansion**
When computing the determinant, choose a row or column that minimizes computation:
### 4x4 Matrix:
\[
\begin{vmatrix}
2 & 8 & -7 & 3 \\
0 & -4 & 9 & -7 \\
0 & 0 & 1 & 2 \\
0 & 0 & 0 & 5 \\
\end{vmatrix}
\]
### Explanation:
This is a 4x4 matrix. To optimize calculation, consider expanding across the last row or column, as it contains zeros which simplify the process.
In this context, the determinant of the matrix is structured as follows (before simplification):
\[
= \begin{vmatrix}
2 & 8 & -7 & 3 \\
0 & -4 & 9 & -7 \\
0 & 0 & 1 & 2 \\
0 & 0 & 0 & 5 \\
\end{vmatrix}
\]
#### Answer Box:
Provide your simplified answer:
__[ ]__ *(Simplify your answer.)*
This exercise illustrates the importance of selecting strategic rows or columns to minimize calculations during cofactor expansion.
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