2.68 I FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICSAlgebra
Example 117 : Find the determinant of the given 3×3 matrix
6 2 4
5 6 2
5 2 3−
(^) −
(^) − (^)
Solution:
det
6 2 4
5 6 2
5 2 3
−
(^) −
(^) − (^)
= 6 det
6 2
2 2
−
(^) − – 2 det
5 2
5 3
−
(^) − + (–4) det
5 6
5 2
(^)
= 6 [ – 18 –(–4)] – 2 [ – 15 (–10)] – 4 [10 – 30]
= 6 (–14) – 2 (–5) – 4 (– 20)
= –84 + 10 + 80
= 6
Example 118 : Find the determinant of the given 3×3 matrix
5 3 4
2 0 2
2 5 1−
(^) −
− (^)
Solution:
det
5 3 4
2 0 2
2 5 1
−
(^) −
(^) − (^)
= 5 det
0 2
5 1
−
(^) − – 3 det
2 2
5 1
−
(^) − + (–4) det
2 0
2 5
(^)
= 5 [0 – (–10)] – 3 [ – 2 – (–4)] – 4 [10 – 0]
= 5 (10) – 3 (2) – 4 (10)
= 50 – 6 – 40
= 4
SELF EXAMINATION QUESTIONS
(1) Evaluate(^87) (Ans. 37)
3 2
−
(2) Evaluate4 2 1
7 3 3 (Ans. 8)
2 0 1