Mathematical Methods and Mechanics

Question I

Consider the simultaneous equations

h*?scz* 5xl=6 n*lxz- 44=7

Lxr + 7xz -124: 12

(a) By using the method of Gauss elimination tnthpartial pivoting only,rcducethe augmented matrixto upper friangular form.

(8 marks)

(b) Hence, using back substitutien, find the solution of the equations. (4 marks)

Question 2

The variable x in a population model satisfies the differential equation

9:a.+*(r- 'l-zsdt ( 1000/ (a) Find the two equilibrium values of the population.

(7 marks)

O) For each of the two equilibrium values, determine whether it is stable or unstable'

(5 marks)