These require a Yes or No answer Which of the following are

These require a Yes or No answer.

Which of the following are spanning sets of P^3? 1..{x+1,x-1,x^2+2} 2.{3,x^2,4-x^2} 3.{1,x2,x,3x+2} 4. (z + 3,x^2 1}

Solution

1.yes

2.no ,cant form x as a linear combination.

3.yes

4.no, not enough elements

1 and 3 can be represented as a+bx+cx^2