Transcript MATLAB

MATLAB
Determinants and Matrices
1
From Format Mesh Analysis
11I1 - 3I2 - 8I3 = 15
-3I1 + 10I2 - 5I3 = 0
-8I1 - 5I2 + 23I3 = 0
2
Solve by determinants
(Set up Matrix A & B)
%Defines the coefficient matrix A
A=[11,-3,-8;-3,10,-5;-8,-5,23;]
A=
11I1 - 3I2 - 8I3 = 15
-3I1 + 10I2 - 5I3 = 0
-8I1 - 5I2 + 23I3 = 0
11 -3 -8
-3 10 -5
-8 -5 23
%defines the vector B
B=[15;0;0]
B=
15
0
0
3
Solve by determinants
(Set up Denominator matrix)
%defines the I1 determinant
D1=A; D1(:, 1)=B
D1 =
%defines the I1 determinant
D3=A; D3(:, 3)=B
D3 =
15 -3 -8
0 10 -5
0 -5 23
11 -3
-3 10
-8 -5
15
0
0
%defines the I2 determinant
D2=A; D2(:, 2)=B
D2 =
11
-3
-8
15 -8
0 -5
0 23
4
Solve By Determinants
(Calculate Currents)
%Calculates I1
I1=det(D1)/det(A)
I1 =
2.6327
%Calculates I2
I2=det(D2)/det(A)
I2 =
1.3998
%Calculates I2
I3=det(D3)/det(A)
I3 =
1.2200
5
Total Determinant Program
11I1 - 3I2 - 8I3 = 15
-3I1 + 10I2 - 5I3 = 0
-8I1 - 5I2 + 23I3 = 0
I1 =
2.6327
I2 =
1.3998
I3 =
1.2200
%This program solves for I1, I2, and I3
diary EENG1920e.dat
%Defines the coefficient matrix A
A=[11,-3,-8;-3,10,-5;-8,-5,23;];
%defines the vector B
B=[15;0;0];
%defines the I1 determinant
D1=A; D1(:, 1)=B;
%defines the I2 determinant
D2=A; D2(:, 2)=B;
%defines the I3 determinant
D3=A; D3(:, 3)=B;
%Calculates I1
I1=det(D1)/det(A)
%Calculates I2
I2=det(D2)/det(A)
%Calculates I2
I3=det(D3)/det(A)
diary
6
Solve By Matrices
%Defines the A Matrices
A=[11,-3,-8;-3,10,-5;-8,-5,23;];
A=
11 -3 -8
-3 10 -5
-8 -5 23
%Defines the B Matrices
B=[15;0;0]
B=
% solve for the loop currents I1 and I2
I = inv(A)*B
I=
2.6327
1.3998
1.2200
15
0
0
7
Total Matrices Program
11I1 - 3I2 - 8I3 = 15
-3I1 + 10I2 - 5I3 = 0
-8I1 - 5I2 + 23I3 = 0
%This program solves for I1, I2 and I3
diary EENG1920d.dat
%Defines the A Matrices
A=[11,-3,-8;-3,10,-5;-8,-5,23;]
%Defines the B Matrices
B=[15;0;0]
% solve for the loop currents I1 and I2
I = inv(A)*B
diary
I=
2.6327
1.3998
1.2200
8