Download MA2200Tutorial Sheet 6

Tutorial Sheet 6
1. Use Gaussian elimination to solve the following systems of simultaneous equations:
(a) x + y = 12
2x + 5y + 2z = 20
6x + 3y + 6z = 0
(b) x + y = 11
2x - 5y + 2z = -6
6x + 3y + 6z = 90
(c) 6x - 7z = 2 - 4y
5z = 9 - 8x - 2y
2x + 6y = 7 - 8z
(d) -3x -4z = -32 - 2y
-2x = 111 - 3y - 8z
y + 6z = 75
(e) 6x - 3y - 2z = 2
2x = 2 - 4y
5x = 7y + 6z
(f) 6x + 4y - 8z = -36
8x + 9y + 2z = 202
3x - 2y + 4z = 102
2. Now use Gauss-Jordan elimination on the equations in the previous question. Check that
your answers are the same.
3. Solve the following simultaneous equations using Cramer’s rule.
(a) 3x + 2y - z = -1
2x + 5y = 16
z=3
(b) x + y + 2z = 3
4x + 2y + z = 13
2x + y - 2z = 9
(c) 2x + y - z = 9
x + 2y + z = 6
3x - y + 2z = 17
(d) 2a + b+ c = 8
5a - 3b + 2c = -3
7a - 3b + 3c = 1
4. Find the equilibrium prices and quantities for the following equations (you may use the
method of your choice):
(a) Qd1 = 30 − P1 + 4P2 , Qs1 = 3P1 − 6
Qd2 = 36 + 3P1 − 2P2 , Qs2 = 12P2 − 4
(b) Qd1 = 50 − 2P1 + 2P2 , Qs1 = 2 + P1
Qd2 = 120 − 4P1 + 6P3 , Qs2 = 3P2 − 2P1
Qd3 = 150 + P2 − 2P3 , Qs3 = 4P 3 − 2P1
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ANS 1. (a) 7,5,-19/2 (b) 5,6,7 (c) 3/4,1/4,1/2 (d) 2,9,11 (e) 1/2,1/4,1/8 (f) 14,6,18 3.
(a)-2,4,3 (b)2,3,-1 (c) 5,0,1 (d) 1,4,2
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