The discussion revolves around finding a basis for the vectors (1, a, a^2), (1, b, b^2), and (1, c, c^2). Participants are exploring the linear independence of these vectors and the implications of the problem statement.
There is ongoing exploration of the problem, with some participants questioning the clarity of the original problem statement. Guidance has been offered on how to manipulate the equations to eliminate variables, though not all participants are comfortable with the approach.
Participants note the need for clarification on the nature of the variables a, b, and c, and express uncertainty about solving the system of equations with general variables rather than specific numbers.
bob258173498 said:Show that for any three distinct values a,b,c, the vectors (1,a,a2), (1,b,b2), (1,c,c2) are linearly independent.
bob258173498 said:Homework Statement
Find a basis for (1, a, a^2) (1, b, b^2) (1, c, c^2)
Homework Equations
The Attempt at a Solution
M(1, a, a^2) + N(1, b, b^2) + K(1, c, c^2) = (0, 0, 0)
M + N + K = 0
Ma + Nb + Kc = 0
Ma^2 + Nb^2 + Kc^2 = 0
This is as far as I got. I tried monkeying around with these 3 equations to no avail.
Yes, it will work in this case.bob258173498 said:Can someone please just show me how to solve it. I don't know how to solve it when the variables are general and not actual numbers. Normally I just get rid of one variable by mult/subtracting equations... but it won't work in this case. Please help!