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
