Page 100 - DMTH201_Basic Mathematics-1

Unit 4: Determinants

Notes
Adj A
Now, A 1
A
| |
1 3 1
1
2 2 2
4
1 5 3

1 1 1 1 3 1
1
AA 1 2 1 0 2 2 2
4
3 2 1 1 5 3

4 0 0 1 0 0
1
0 4 0 0 1 0 I
4
0 0 4 0 0 1
AA 1 I

1
Similarly it can be verified that A A . I
1
AA 1 A A . I
4.9 Examples on Simultaneous Equations (Cramer’s Rule)

Example: Using Cramer’s Rule, solve the following equations:
1. 3x 4y 7, 4x 3y 5

2. 3x 3y 12, 2x 4y 12
3. 6x 4y 10, x 7y 8
4. x 6y 16, 2x 3y 13
5. 2x y 4, 3x 4y 11
6. x y z 11, 2 x 6 y z 0, 3 x 4 y 2 z 0

7. x 3y z 4, x 2z 5, 3x y 5
8. z 2x 1 0, y z 2 0, x 2y 5
Solution:

1. 3x 4y 7

4x 3y 5

3 4
9 16 25
4 3

7 4
21 20 41
1
5 3

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