Overdetermined system of equations

My equation looks as follows: Y = x1*A + x2*B + x3*C, where Y, A, B, C are matrices of the 260x100 dimension and I want to solve for x1 , x2 , x3 but I'm not sure how to approach this in Matlab. Could someone share some tips with me, please ?

[John D'Errico]

Are x1,x2,x3 scalar unknowns? Are they arrays?

[Damian Wierzbicki]

They're scalar unknowns

Answer 1

[John D'Errico]

So you have only 3 unknowns.

x123 = [A(:),B(:),C(:)]\Y(:);

This returns a vector of length 3, which is the linear least squares solution.

[Damian Wierzbicki]

Thank you :)

[Damian Wierzbicki]

What if I had another equation that looks as follows: Z = x1*D + x2*E + x3*F, where Z, D, E, F are again matrices of the same size as above and x1, x2, x3 are defined as above. When I solve them separately, they give me two different set of solutions, as expected. How can I combine the two equation, so I get one set of solutions for both systems ? Adding both sides of the equation and then solving for x1, x2, x3 ? I'd be really grateful if you could help.

[Torsten]

x123=[A(:),B(:),C(:);D(:),E(:),F(:)]\[Y(:);Z(:)];

Best wishes

Torsten.

[Damian Wierzbicki]

Thank you !