How to find inverse of a non square matrix?

Hello I have some a (91x1) array x and (91x2) array y. i need to find two constants a1, a2 which basically make a (2x1) array.

my equation is x=y*a , where a is the 2x1 matrix. my matrix dimensions match but i am unsure how to solve this equation for the values of a1 and a2.

Edited: additional condition is that the values a1 and a2 should sum to 1. it can be assumed that y has values greater y. Any help will be appreciated.

Answer 1

[Matt J]

Although it may be overkill for such a small problem, you could also use lsqlin,

a = lsqlin(y,x,[],[], [1,1],1 ,[0,0],[1,1]);

[Muneeb Aizaz]

so this is satisfying the conditions that a1+a2=1 and a1 and a2>0 ?

[Bruno Luong]

Almost a1 and a2 >= 0 (not strictly positive), if you like to use a big hammer. Otherwise look at the solution I propose above.

Answer 2

[Bruno Luong]

unconstrained solution

a = y \ x

[Muneeb Aizaz]

Sorry there is one additional condition that the values a1 and a2 should sum upto 1.

[Bruno Luong]

constraints a1+a2 = 1

a2 = diff(y,1,2)\(x-y(:,1));
a1 = 1-a2;

[Bruno Luong]

constraints a1+a2 = 1, and a1, a2 >= 0

a2 = diff(y,1,2)\(x-y(:,1));
a2 = min(max(a2,0),1);
a1 = 1-a2;

Answer 3

[KSSV]

x = rand(91,1) ;
y = rand(91,2) ;

a = y\x

[Muneeb Aizaz]

Sorry there is one additional condition that the values a1 and a2 should sum upto 1.