# Plotting of null surfaces and Warning: Matrix is singular to working precision.

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Vira Roy on 18 Dec 2019
Commented: David Goodmanson on 22 Dec 2019
Problem: I have the following three sets of equation which i need to plot as planes in 3D system.
I ,N and T are there variables representing the null surfaces .Now i don't have to solve them, instead i just have to plot them as planes and see their intersections. Here is the plot i am supposed to get,
My attempt: I tried to use meshgrid and surf to plot the plane but i don't understand how to proceed with the first two. The third one i tried like
[T N] = meshgrid(0:0.01:5);
I= (0.33*(0.3+T))/((T+0.2)*(0.3+T)-0.01*T);
surf(T,N,I);
This led me to a warning: Matrix is singular to working precision. I checked if somewhere the denominator vanishes but they don't.
For the second i tried:
[I N] = meshgrid(0:0.01:5);
T= 1-I/3-N/1.5;
surf(I,N,T);
But again this did give something but nothing like the above figure. I could be completly wrong with my attempt here, hence any guidance or a small code will be extremely helpful. The variable I, T, and N are Immune, Tumor and Normal in the above figure.
Thank you.
David Goodmanson on 22 Dec 2019
Hi Vira,
I don't believe the second and third equations correspond to the figure in your question. For the third equation, if you plug in T = 0 you get 1.5 for any N, but the figure shows 5. For the second equation, if you plug in N=0 T=0 you get 3, but the figure (up from the back corner where you can't actually see the origin T=0,N=0) shows 9.

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