How to write cramer's rule 3x3 by matlab ?

How to write cramer's rule 3x3 by matlab ?

[James Tursa]

What have you done so far? Do you know how to replace elements in a matrix with other elements? Do you know how to use a for loop? Do you know how to calculate the determinant of a matrix?

Answer 1

[Explorer]

Question: Find the system of Linear Equations using Cramers Rule:

2x + y + z = 3

x – y – z = 0

x + 2y + z = 0

The above example is taken from http://www.purplemath.com/modules/cramers.htm

% Demo Code:

A = [2 1 1; 1 -1 -1; 1 2 1]     % Coefficient Matrix
X = [3; 0; 0]

Ax = [3 1 1 ; 0 -1 -1;0 2 1 ] 
Ay = [2 3 1; 1 0 -1; 1 0 1]
Az = [2 1 3; 1 -1 0; 1 2 0]

detA=det(A)

x = det(Ax)/detA
y = det(Ay)/detA
z = det(Az)/detA

[Batool Alfaraj]

How did you do the Ax, Ay, Az?

[James Tursa]

By selectively replacing a column of A with X. Ax has 1st column replaced, Ay has 2nd column replaced, Az has third column replaced.

[Robert Strunz]

Is there not a tider way of replacing columns in a matrix than this?

[Robert Strunz]

Is this a better solution,my matrix is called NAM, and the column vector is I ?

% Create a modified NAM for node b by inserting I into the first column.
mNAM_b = [I NAM(:,2:3)]
delta_b = det(mNAM_b)
VB = delta_b/delta_0

% Create a modified NAM for node c by inserting I into the second column.
mNAM_c = [NAM(:,1) I NAM(:,3)]
delta_c = det(mNAM_c)
VC = delta_c/delta_0

% Create a modified NAM for node e by inserting I into the third column.
mNAM_e = [NAM(:,1) NAM(:,2) I]
delta_e = det(mNAM_e)
VE = delta_e/delta_0

[James Tursa]

Rather than creating the modified matrix with concatenation, a direct assignment of the column:

k = the column number to replace
mNAM = NAM;
mNAM(:,k) = I;

This could easily be put into a loop.

[Sebastián]

This is my solution

%original matrix
x=[2 1 1;1 -1 -1;1 2 1]
res=[3 0 0]
detx=det(x)
sx=length(x)
ans=zeros(1,sx)
sistem=repmat(x,1,1,3);
%replace independent matrix in original matrix
for i=1:1:sx
    sistem(:,i,i)=res;
    ans(:,i)=det(sistem(:,:,i))/detx;
end
disp(ans)

Answer 2

[Faith Ira Daro]

given the linear equations:

3x+2y = -5

-5x+7y=1

solve for the values of x and y using cramers rule

Answer 3

[Asif Iqbal]

% Demo Code:

A = [2 1 1; 1 -1 -1; 1 2 1] % Coefficient Matrix

X = [3; 0; 0]

Ax = [3 1 1 ; 0 -1 -1;0 2 1 ]

Ay = [2 3 1; 1 0 -1; 1 0 1]

Az = [2 1 3; 1 -1 0; 1 2 0]

detA=det(A)

x = det(Ax)/detA

y = det(Ay)/detA

z = det(Az)/detA