Page 101 - MATLAB an introduction with applications

86 ——— MATLAB: An Introduction with Applications

y

z
+
x 1.1 2 5
x 2
z
y
A= + a
ab
(+ ) b /3 z a
P1.8: Enter the following three matrices in MATLAB
1 2 3 12 5 4 7 13 4

A 85 7 , B 7 11 6 , C 2 8 5

846 1 8 13 9 6 11
and show that
(a) A + B = B + A
(b) A + (B + C) = (A + B) + C
(c)7(A + C) = 7(A) + 7(C)
(d) A * (B + C) = A * B + A * C
P1.9: Consider the polynomials
3
2
p (s) = s + 5s + 3s + 10
1
2
p (s) = s + 7s + 5s + 8s + 15
4
3
2
p (s) = s + 15s + 10s + 6s + 3s + 9
4
5
3
2
3
Determine p (2), p (2) and p (3).
3
2
1
P1.10: The following polynomials are given:
p (x) = x + 2x – 3x + 7x – 8x + 7
5
2
3
4
1
3
2
4
p (x) = x + 3x – 5x + 9x + 11
2
2
3
p (x) = x – 2x – 3x + 9
3
2
p (x) = x – 5x + 13
4
p (x) = x + 5
5
Use MATLAB functions with polynomial coefficient vectors to evaluate the expressions at x = 2.
P1.11: Determine the roots of the following polynomials:
2
7
5
6
4
3
(a) p (x) = x + 8x + 5x + 4x + 3x + 2x + x + 1
1
2
6
(b) p (x) = x – 7x + 7x + 15x – 10x – 8x + 7x + 15
4
5
3
6
2
2
3
5
4
(c) p (x) = x – 13x + 10x + 12x + 8x – 15
3
2
3
4
(d) p (x) = x + 7x + 12x – 25x + 8
4
(e) p (x) = x + 15x – 23x + 105
3
2
5
2
( f ) p (x) = x – 18x + 23
6
(g) p (x) = x + 7
7
P1.12: An aluminium thin-walled sphere is used as a marker buoy. The sphere has a radius of 65cm and
3
a wall thickness of 10 mm. The density of aluminium is 2700 kg/m . The buoy is placed in the ocean where
3
the density of the water is 1050 kg/m . Determine the height H between the top of the buoy and the surface
of the water.
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