Question

The equation for the thermal expansion coefficient, α = ai + a2T+437', is obtained using regression analysis where the constants of the model are found by solving the following simultaneous linear equations 1. 24 - 2860 7.26x 105 h] 「 1.057x10" 2860 7.26x10-1.86472x101.04162x10-2 7.26x10 -1.86472x10 524357x10 a Find the values of ai , a2, and a3 using naive Gauss elimination. 2.56799 (10 marks)

Answer 1

BASED ON THE GIVEN DATA, WE CAN FINDTHE VALUES OF A₁,A₂,A₃ USING NAIVE GAUSS ELIMINATION BY USING MATLAB CODE

MATLAB CADE :-

CLOSE ALL

CLEAL

CLC

a = [24 -2860 7.26*1e5;
-2860 7.26*1e5 -1.86472*1e8;
7.26*1e5 -1.86472*1e8 5.24357*1e10];
b = [1.057*1e-4;-1.04162*1e-2;2.56799];
a = inv(A)*b;

printf('a1 = %f\na2 = %f\na3 = %f\n\n', a);
deltaD = 12.363*integral(@(t)a(1)+a(2)*t+a(3)*t.^2,80,-108)

OUTPUTWILL BE AS BELOW

A₁  = 0.000005
A₂  = 0.000000
A₃ = -0.000000

deltaD = -0.0116