Page 85 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes 1
A is determined by using the formula
Adj .A
A 1 where | | 0.
A
A
| |

Notes If A is inverse of B, then B is also inverse of A.

4.7 Solution of a System of Linear Simultaneous Equations

(Cramer’s Rule)

1. To solve the simultaneous equations in two variables:

a x b y c 1 ...(1)
1
1
a x b y c 2 ...(2)
2
2
a b
Find 1 1 a b a b 0.
a 2 b 2 1 2 2 1

Replace a a by , c to get
c
,
1 2 1 2
c 1 b 1
2 1
1 2
1 c b c b
c b
2 2
Replace b b 2 by , c to get
,
c
2
1
1
a 1 c 1
2 a c a c
1 2
2 1
a 2 c 2
Then by Cramer’s Rule
x 1 and y 2 .
2. To solve the simultaneous equations in three variables
a x b y c z d 1
1
1
1
a x b y c z d 2
2
2
2
a x b y c z d 3
3
3
3
a b c
1 1 1
Find a 2 b 2 c 2 0.
a b c
3 3 3
,
d
,
,
Replace a a a 3 by , d d 3
2
1
1
2
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