PROBLEM #1:
Problem 1: Use Cramer's Rule to solve for x Check answer using backslash operator
Coefficient Matrix
A = (12 4 11 9;
7 3 1 18;
6 24 21 8;
8 13 10 1);
%Right hand side vector
b=(8;
20;
42;
25];
Cramer's Rule
determinant
disp('Solving by Cramers Rule')
D=det(A);
Al-A;
A1(:,1)=b; %replace first column of 'Al' by 'b' x1 = det(A1)/D
A2 A; 'b'
A2(:,2) = b; %
x2 = det(A2)/D replace second column of 'A2' by 'b'
A3 = A;
A3(:,3) = b; %
x3 = det(A3)/D replace first column of 'A3' by 'b'
A4 = A;
A4(:,4) = b; % replace first column of 'A4' by 'b'
x4 = det(A4)/D
Solving by Cramers Rule
x1 = 0.3787
x2 = 2.4795
x3 = -1.0874
x4 0.6110
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PROBLEM #2:
a) Use Cholesky decomposition to find upper triangular matrix U
b) Use U to solve for the stresses in the material for 3 different experiments
E = 750; %Modulus of Elasticity--->Gpa
v = 0.4; %Poisson's Ratio
% Coefficient Matrix
A = (1 -v -v;
-v 1 -17:
-v -v 1);
U = a chol(A)
%Coefficient Matrix
A = (1 -v -v;
- v 1 -v;
- v -v 1);
el = 0.001;
e2 = 0.003:
e3 = 0.020;
%Eight hand side vector
b = (el e2 e3)
U = chol(A)
x = (b*E)/U
%coefficient Matrix
A a (1 -v -v;
- v 1 -v;
- v -v 1):
el = 0.004;
e2 = 0.006:
e3 = 0.006;
%Right hand side vector b = (el e2 e3);
U = chol(A);
x = (b*E)/U
%Coefficient Matrix
A = (1 -v -v;
-v 1 -v:
-v -v 11:
e1 = 0.050:
e2 = 0.070:
e3 = 0.010:
%Right hand side vector
b = [e1 e2 e3]:
U = chol(A):|
x = (b*E)/U
3.0000 7.855e 15.3709
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