Page 109 - MATLAB an introduction with applications

94 ——— MATLAB: An Introduction with Applications

(b) x – x + 3x + 5x =7
3
4
2
1
2x + x – x + x =6
3
1
2
4
–x – x – 2x + 2x =5
2
4
3
1
x + x – x + 5x =4
1
2
4
3
P1.51: Solve the following set of equations using MATLAB.
(a) 2x + x + x – x =10
1 2 3 4
x + 5x – 5x + 6x =25
1 2 3 4
–7x + 3x – 7x – 5x = 5
3
1
2
4
x – 5x + 2x + 7x =11
4
3
2
1
(b) x – x + 3x + 5x =5
1
2
3
4
2x + x – x + x =4
3
2
1
4
–x – x + 2x + 2x =3
2
3
4
1
x + x – x + 5x =1
2
4
3
1
P1.52: Solve the following set of equations using MATLAB.
(a) x + 2x + 3x + 5x =21
1 2 3 4
–2x + 5x + 7x – 9x =17
2
1
4
3
5x + 7x + 2x – 5x =23
2
3
1
4
–x – 3x – 7x + 7x =26
3
4
1
2
(b) x + 2x + 3x + 4x =9
1
4
2
3
2x – 2x – x + x =–5
4
2
1
3
x – 3x + 4x – 4x =7
1
2
4
3
2x + 2x – 3x + 4x =–6
4
1
3
2
P1.53: Determine the inverse of the following matrix using MATLAB.
 3s 2 0 
A =  7s − s − 5 
 
  3 0 − 3s 
P1.54: Expand the following function F(s) into partial fractions with MATLAB:
5s + 7s + 8s + 30
3
2
() =
Fs
s + 15s + 62s + 85s + 25
3
2
4
P1.55: Determine the Laplace transform of the following time functions using MATLAB.
(a) f (t) = u (t + 9)
(b) f (t) = e 5t
(c) f (t) = (5t + 7)
(d) f (t) = 5u (t) + 8e – 12e –8t
7t
3
–t
–2
(e) f (t) = e + 9t – 7t + 8
( f ) f (t) = 7t + 5t – e –7t
4
2
(g) f (t) = 9 u t + 5e –3t
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