Paper 4: Fundamentals of Business Mathematics & Statistic

FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 2.67

Solution:

det

2 3 2

6 3 3

2 3 2

− −

(^) −
(^) − − − (^)
= 2 det

3 3

3 2

(^) − − – (–3) det

6 3

2 2

−

(^) − − + (–2) det

6 3

2 3

−

(^) − − (^)
= 2 [– 6 – (– 9)] + 3 [12 – (–6)] – 2 [18 – (– 6)]
= 2 (3) + 3 (18) – 2 (24)
= 12
Example 115 : Find the determinant of the given 3×3 matrix
4 5 2
3 4 2
1 2 5

−

(^) −
(^) − (^)
Solution:
det

4 5 2

3 4 2

1 2 5

−

(^) −
(^) − (^)
= – 4 det

4 2

2 5

• 4 det

3 2

1 5

−

(^) − − + 2 det

3 4

1 2

−

(^) − − (^)

= – 4 [20 – 4] – 5 [ – 15 – (–2)] + 2 [ – 6 –(– 4)]

= – 4 (16) – 5 (–13) + 2 (– 2)

= − 3

Example 116 : Find the determinant of the given 3×3 matrix

1 3 6

1 5 5

1 6 5

− −

(^) −
(^) − (^)
Solution:
det

1 3 6

1 5 5

1 6 5

− −

(^) −
(^) − (^)
= 1 det

5 5

6 5

• 3 (–3) det

1 5

1 5

−

(^) − + (–6) det

1 5

1 6

−

(^) − (^)

= 1[25 – 30] + 3 [ – 5 (–5)] – 6 [ – 6 –(– 5)]

= 1 (–5) + 3 (0) – 6 (– 1)

= − 1