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## Homework Statement

Let U be the subspace of P3(ℝ) spanned by

E={x^3,x^3-x^2,x^3+x^2,x^3-1}

find a linearly independent subset F of E spanning U.

## Homework Equations

E={x^3,x^3-x^2,x^3+x^2,x^3-1}

## The Attempt at a Solution

a(x^3)+b(x^3-x^2)+c(x^3+x^2)+d(x^3-1)=0x^3+0x^2+0x+0

(a+b+c+d)x^3+(-b+c)x^2+(-d)=0x^3+0x^2+0x+0

a+b+c+d=0

-b+c=0

-d=0

a=-2b, b=c, d=0

t(-2,1,1,0), t[itex]\in[/itex]ℝ

How do I figure out which vectors are linearly independent??