482 Chapter 17Determinants
Each of the third-order determinants can be evaluated by the method described in
Section 17.2; that is, by expansion in minors of order 2. Then, expanding each along
the first row,
D 1 =
= 121 × 151 − 111 × 1 (−9) 1 + 111 × 1 (−29) 1 − 131 × 121 = 1 − 16
0 Exercises 11–13
EXAMPLE 17.7Find the value of the ‘triangular’ determinant
Expansion along the first column gives
The value of a triangular determinant is equal to the product of the elements on the
diagonal,
D 1 = 1 a
111 × 1 a
221 × 1 a
331 ×1-1× 1 a
nn.
0 Exercise 14
=× × 1610 =× × × ×
13 14
015
1 6 10 13 15
D== 1 ×
6789
0101112
0 0 13 14
00015
16
10 11 12
01314
00155
D=
12 3 4 5
06789
0 0 10 11 12
00 01314
00 0 015
−−−
−
−
34
10
31
2
10
01
0
11
03
()
−
−−
−
−
−
14
12
31
2
12
01
1
11
03
()
−
−
−
−
−
−
14
02
11
0
12
01
1
10
01
−
−
−
−
22
02
11
0
12
31
1
10
31