Find Linear Combinations for {1, x, x^2, x^3}

[FrostScYthe]

{1, x, x(x-1), x(x-1)(x-2)} you want to find the linear combinations that will give you 1, x, x^2, x^3

a + a(x) + a(x(x-1)) + a(x(x-1)(x-2)) = 1
a + a(x) + a(x(x-1)) + a(x(x-1)(x-2)) = x
a + a(x) + a(x(x-1)) + a(x(x-1)(x-2)) = x^2
a + a(x) + a(x(x-1)) + a(x(x-1)(x-2)) = x^3

I don't know what to do from there

 

[matt grime]

I think you might not want to call the constants all 'a'.

1=1
x=x
as for the others trying writing out x(x-1) as something easier to work with

 

[ComputerGeek]

If you set up an appropriate matrix and augmenting it with the answers you want, row reduction should give you your answers.