12 different coordinates for 12 equations, how to do it quickly?

I have 12 different coordinates: (x,y)= (1,1) , (-1,1) , (-1,-1) etc

I need to plug one coordinate into 12 different equations, for example:

x+y=w

2x+2y=w+m

3x+3y=v+m

and so on. I need to do this for all 12 different coordinates. How can I do this quickly without having to set up 12*12 = 144 equations?

...

[James Tursa]

Can you please give us context? What is the overall problem that you are solving? How do you have your coordinates and your equations stored/represented in MATLAB?

[Ruslan Khoguev]

I have this code, where xi and eta is x and y coordinates respectively. I have a set of coordinates which need to be plugged into the equations below N(2), N(3)...N(12) and get a scalar value. I wish to find the value of the equations for varying coordinates. Please let me know if anything is unclear. How

a=1;
b=1;                
xi=1;                       %varying
eta=1;                     %varying
N(2)=-b*(xi-1)*(eta-1)^2*(eta+1)/8;
N(3)=a*(xi-1)^2*(eta-1)*(xi+1)/8;
N(5)=b*(xi+1)*(eta-1)^2*(eta+1)/8;
N(6)=a*(xi+1)^2*(eta-1)*(xi-1)/8;
N(8)=b*(xi+1)*(eta+1)^2*(eta-1)/8;
N(9)=-a*(xi+1)^2*(eta+1)*(xi-1)/8;
N(11)=-b*(xi-1)^2*(eta+1)^2*(eta-1)/8;
N(12)=-a*(xi+1)*(eta+1)*(xi-1)^2/8;
N(1)=(xi-1)*(eta-1)/4+N(2)/(2*b)-N(3)/(2*a)-N(6)/(2*a)+N(11)/(2*b);
N(4)=-(xi+1)*(eta-1)/4+N(3)/(2*a)+N(5)/(2*b)+N(6)/(2*a)+N(8)/(2*b);
N(7)=(xi+1)*(eta+1)/4-N(5)/(2*b)-N(8)/(2*b)+N(9)/(2*a)+N(12)/(2*a);
N(10)=-(xi-1)*(eta+1)/4-N(11)/(2*b)-N(12)/(2*a)+N(9)/(2*a)+N(2)/(2*b);

[Jan]

@Ruslan: I still do not get it. What should be a scalar value? What does "plugging in" mean? What is "a value of 12 equations"? What does "varying" mean? Do you want to write this in form of a matrix equation? Then you can solve it for the vectors xi and eta.

[Ruslan Khoguev]

I wish to calculate N(2), N(3)...N(10) for (xi,eta)= (1,1) , (-1,1) , (-1,-1). What is the fastest way to do this.

[Walter Roberson]

10 vectorized equations with input built by ndgrid or meshgrid.

[Ruslan Khoguev]

Could you show an example of this? I am new to MATLAB

[Walter Roberson]

[eta, xi] = ndgrid(-1:1, -1:2);

N3=a*(xi-1).^2.*(eta-1).*(xi+1)/8;