1. Use a cofactor expansion to compute the following determinants. 2 -1 0-1 -1 2-1 3 (a) 2 0 0 4 3 2 5 -1 1 3 5 (b) 2 1 1 34 2 (c) 7072 0-1 2-1 -1 0 -1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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1. Use a cofactor expansion to compute the following determinants.
2 -1 0 -1
-1
2-1 0
0 -1
2 -1
2
3
(a) 2
0
0
4
3
2
5 -1
1 3 5
1
1
4
2
(b) 2
(c)
-1
0 -1
Transcribed Image Text:1. Use a cofactor expansion to compute the following determinants. 2 -1 0 -1 -1 2-1 0 0 -1 2 -1 2 3 (a) 2 0 0 4 3 2 5 -1 1 3 5 1 1 4 2 (b) 2 (c) -1 0 -1
Expert Solution
Step 1

The determinants are given as 

(a) 30423205-1

(b) 135211342

(c) 2-10-1-12-100-12-1-10-12

The aim is to compute the determinants using cofactor expansion.

Concept Used: 

If A is a n×n matrix, then the determinant of the matrix, expanded with respect to the first row is calculated by the formula det A=i=1na1iA1i, where A1i is the cofactor with respect to the element a1i in the first row.

Cofactor of an element is calculated by the formula Aij=(-1)i+jMij, where Mij is the minor with respect to the element.

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