Higher Engineering Mathematics

THE SOLUTION OF SIMULTANEOUS EQUATIONS BY MATRICES AND DETERMINANTS 285

F

3. From equation (3′′),

I 3 =

− 89. 308

− 9. 923

=9mA,

from equation (2′),− 6. 5 I 2 − 9 =−100,

from which,I 2 =

− 100 + 9

− 6. 5

=14 mA

and from equation (1), 2I 1 +3(14)−4(9)=26,

from which,I 1 =

26 − 42 + 36

2

=

20

2

=10 mA

Now try the following exercise.

Exercise 116 Further problems on solv-

ing simultaneous equations using Gaussian

elimination

1. In a mass-spring-damper system, the acceler-
   ation ̈xm/s^2 , velocity ̇xm/s and displacement
   xm are related by the following simultaneous

equations:

6. 2 ̈x+ 7. 9 x ̇+ 12. 6 x= 18. 0

7. 5 x ̈+ 4. 8 x ̇+ 4. 8 x= 6. 39

13. 0 x ̈+ 3. 5 ̇x− 13. 0 x=− 17. 4

By using Gaussian elimination, determine the

acceleration, velocity and displacement for

the system, correct to 2 decimal places.

[ ̈x=− 0 .30,x ̇= 0 .60,x= 1 .20]

2. The tensions, T 1 ,T 2 and T 3 in a simple
   framework are given by the equations:
   5 T 1 + 5 T 2 + 5 T 3 = 7. 0
   T 1 + 2 T 2 + 4 T 3 = 2. 4
   4 T 1 + 2 T 2 = 4. 0
   Determine T 1 ,T 2 and T 3 using Gaussian
   elimination.
   [T 1 = 0 .8,T 2 = 0 .4,T 3 = 0 .2]


3. Repeat problems 3, 4, 5, 7 and 8 of Exer-
   cise 113 on page 279, using the Gaussian
   elimination method.


4. Repeat problems 3, 4, 8 and 9 of Exercise 114
   on page 282, using the Gaussian elimination
   method.