How to create a specific vector c that has two variables x and y ?

the problem here is this vector must be found from c = A\b. A and b are created from two variables x and y. (I posted the image of example xi,yi). x and y come from the normal parabola(ax^2 + bx +c) first, then they could be used in the matrix to form A and b. if my question is too confusing, just see the image...sorry, I am not good at explaining a problem :c Is there a way to solve it ? Thank you.

[Roger Stafford]

Your question is puzzling. You seem to have solved your own question by writing the equation c = A\b. That is a valid matlab operation and is presumably the answer you are seeking. You have three linear equations in three unknowns, a, b, and c, and your matlab expression is how you solve such a problem in matlab. The only difficulty that might occur is if the matrix A of coefficients happened to be singular, that is, its determinant were equal to zero, in which case there might either be no solution or perhaps many solutions.

[CodeElinesa]

yh, i know, if the problem just asks me to use the example x,y values to create c vector, that would be simple. The question is, is there a way to represent the A,b matrix so that any x,y variable could be used?

[CodeElinesa]

at this moment, I create c = parabola(x,y) for further usage Sorry, I forgot to say input vector x and y are only required to be length 3

Answer 1

[Roger Stafford]

Assume your xi's and yi's are given by a couple of column vectors, x and y of the same length.

n = length(x);
A = [x.^(n-1:-1:0)];
c = A\y;

[CodeElinesa]

I don't think it makes sense, because you can check my image, A must be 3x3 matrix, and b is 3x1, and what about x^2?

[Roger Stafford]

If you have an older version of matlab, use

A = bsxfun(@power,x,((n-1):-1:0));

where again I assume x is a column vector.