)| -3,3 2 9 -3 = 2 = 2(1) || 0 0 0 = 2 2( expand along C₁ 0 21 0 = 20 -1 N -4 1 5 3 1 -2 1 4 2 x 7 -4 1 -1 5 4 -3 2 -1 1 9 -3 1 -2 1 2 R₂ - 2 R₁ R3 + R₁ R4 + 3 R₁ expand (along C₁) R₁ + 4 R₂ R3-5 R₂.
)| -3,3 2 9 -3 = 2 = 2(1) || 0 0 0 = 2 2( expand along C₁ 0 21 0 = 20 -1 N -4 1 5 3 1 -2 1 4 2 x 7 -4 1 -1 5 4 -3 2 -1 1 9 -3 1 -2 1 2 R₂ - 2 R₁ R3 + R₁ R4 + 3 R₁ expand (along C₁) R₁ + 4 R₂ R3-5 R₂.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please answer the last one
Transcribed Image Text:)| -3,3
2
9 -3
= 2
11
0
0
0
= 2(
expand
along C₁
O
0
= 20
N
= 2(1) 1 -1
3
-4 1
-1
Y
1
5
4
1 -2
1
5 4 2
-4
21 -1
319
-
-3 2
1
9 -3
x
-2
1
2
R₂ - 2 R₁
R3 + R₁
R4 + 3 R₁
expand
(along C₁)
R₁ + 4 R₂
R3-5 R₂.
Transcribed Image Text:If we want to be really creative (and efficient), we can use a combination of
row/column operations and cofactor expansion to compute the determinant of a
square matrix:
Example: Evaluate the determinant of
2 5
NO
7
0 1
-2-3
4
2
2
0
-2
4
2
5
1
-29
-23
NOW
-3
9 -13
2
2
3
4
0
-7 -2
19 = 0 2
9 13 14
2
6 4
7
2
-7 -2
13
6
= 2
= 2
0-3
10
0
2
3
7
0 -1 -1 -4 -3
-1 -5
-10
4
6
12
2
0
9
3 4
19
14 -29
4 -23
-13
720
1 2 3
0
7
-1 -1 -4 -3
-3
-1 -5
1
2 3
0
1
-1
-4
1
5
9
-13
4
6
4
st
-10
4
-2
1
2
R3 + R₁
R4-2 R₁
R₁ - R₁
expand
along C₁
R₂-2 R₁
R3 + R₁
R4 + 3 R₁
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