Page 88 - DMTH201_Basic Mathematics-1

Unit 4: Determinants

Notes
x 2 x 2
Example: If 3 5 8 is singular, find the value of x.
x 1 7 x 12

Solution:
The given matrix is singular its determinant = 0

x 2 x 2
i.e., 3 5 8 0
x 1 7 x 12

x (60 56 8 ) 2(36 8x 8) ( x 2)(21 3 x 5 x 5) 0
x
4x 8x 2 56 16x 16x 32 8x 2 16x 0

20x 24 0

24 6
x .
20 5

Example: Evaluate the following determinants

40 41 42 77 78 79
20 21
1. 2. 41 42 43 3. 75 74 73
22 23
42 43 44 76 75 74

12 0 0
4200 4201
4. 5. 4 3 0
4202 4203
2 2 3
Solution:

20 21
1. Let
22 23

R 1 R 2

2 2
22 23

C C
1 2
0 2
1 23

Expand

0(23) ( 1)( 2) 2

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