How can I draw the graph for this system of linear equation in MATLAB?

A=[1 2 4; 5 7 9; 10 11 12]
B=[2;4;7]
X=inv(A)*B

Now what can I do to make the graph for this system of linear equation? I mean i need a graph from which we can easily understand the intersecting points.

Answer 1

[Aashray]

Hi @PULAK Kumer!

I understand that you are trying to visualize the solution of a system of linear equations using matrices A and B. One way you can approach this problem is plotting three planes represented by each equation and showing their intersection point, which is the solution to Ax = B.

You can refer to the following script for your query:

A = [1 2 4; 
    5 7 9; 
    10 11 12];
B = [2; 4; 7];

[x, y] = meshgrid(-10:1:10, -10:1:10);

% Extract coefficients from A and B
a1 = A(1,1); b1 = A(1,2); c1 = A(1,3); d1 = B(1);
a2 = A(2,1); b2 = A(2,2); c2 = A(2,3); d2 = B(2);
a3 = A(3,1); b3 = A(3,2); c3 = A(3,3); d3 = B(3);

% Solve for z in terms of x and y: ax + by + cz = d  => z = (d - ax - by)/c
z1 = (d1 - a1*x - b1*y)/c1;
z2 = (d2 - a2*x - b2*y)/c2;
z3 = (d3 - a3*x - b3*y)/c3;

% Solve the system
X = A\B;

% Plot
figure;
surf(x, y, z1, 'FaceAlpha', 0.5, 'EdgeColor', 'none'); hold on;
surf(x, y, z2, 'FaceAlpha', 0.5, 'EdgeColor', 'none');
surf(x, y, z3, 'FaceAlpha', 0.5, 'EdgeColor', 'none');

% Plot intersection point
plot3(X(1), X(2), X(3), 'ko', 'MarkerSize', 10, 'MarkerFaceColor', 'r');

xlabel('x'); ylabel('y'); zlabel('z');
title('Intersection of Three Planes from System Ax = B');
legend('Plane 1', 'Plane 2', 'Plane 3', 'Solution Point');
grid on; axis equal; view(3);

The point where all three planes intersect, that is the solution!

PS: The “FaceAlpha” parameter used in “surf” function modifies the transparency of the plot. You can read more about it from MathWorks documentation : https://www.mathworks.com/help/matlab/ref/surf.html