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1. ### Proof that LHS coefficients have to = RHS coefficients

Yes I meant for all x≠y. Thanks for your help.
2. ### Proof that LHS coefficients have to = RHS coefficients

Sorry, x and y are just real numbers. Such as -12.12, 20, 5080.892, etc. This is not of the form (a)x + (b)y = (c)x + (d)y Unfortunately I still don't see what's wrong with the matrix that I typed up. Not that you're wrong, I just can't understand what you're saying because my maths...
3. ### Proof that LHS coefficients have to = RHS coefficients

Hey everyone. Thanks for so much help on this question. I need to prove this as part of a broader question in an assignment on utility theory. The equation is this; aE[u(x)] + (1-a)E[u(y)] = (b+(1-b)a)E[u(x)] + (1-b-(1-b)a)E[u(y)] (1) Both sides are a gamble, E[u(G(x,y;a))] =...
4. ### Proof that LHS coefficients have to = RHS coefficients

Hi, thank you for your suggestion. Are you sure that this is a proof? I'm not sure; [x y] = [x y], hence [a b] = [c d], hence a=c, b=d I mean it makes complete sense but it's a part of a much longer proof for an assignment so it's important that it's correct
5. ### Proof that LHS coefficients have to = RHS coefficients

Homework Statement If; a*x + b*y = c*x + d*y x ≠ y a,b,c,d ≥ 0 Prove that; a=c b=d 2. The attempt at a solution I've been fiddling with this equation and have been getting nowhere.