Page 86 - DMTH201_Basic Mathematics-1

Unit 4: Determinants

Notes
d 1 b 1 c 1
d b c
1 2 2 2
d b c
3 3 3
b
,
,
Replace b b 2 , by , d d 3
d
2
3
1
1
a d c
1 1 1
a d c
2 2 2 2
a 3 d 3 c 3
d
,
,
Replace c c c by , d d
,
1 2 3 1 2 3
a 1 b 1 d 1
a b d
3 2 2 2
a b d
3 3 3
Then by Cramer’s Rule,
x , y 2 , z .

Tasks Evaluate the following determinants

1 3 1
5 3
1. 2. 2 0 1
2 1
4 5 1
3 4 x
x
Example: If 2 1 3 40, find .
5 1 2
Solution:
3 4 x
2 1 3 40
5 1 2

3(2 3) 4(4 15) x ( 2 5) 40

15 76 3x 40

3x 40 76 15

3x 21

x 7

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