Decide if each is a basis for $P_2$. (a) $(x^2 + x - 1, 2x + 1, 2x - 1)$ I'm using Linear Algebra by Jim Hefferon (freely available, links below with solution).
I'm having trouble understanding Exercise 1.18 on page 117.
1.18 Decide if each is a basis for $P_2$.
(a) $(x^2 + x - 1, 2x + 1, 2x - 1)$
First, I try to prove that it spans $P_2$ $(ax^2 + bx + c)$. However, I do not understand how to set up the matrix. I usually do not have any trouble when there are column vectors given to me and I simply have to row-reduce using Gauss' Method, however whenever given equations with variables I have trouble. 
Can someone walk through this step by step? That would be really helpful. I'm trying to teach myself Linear Algebra so there may be many missing gaps of knowledge.
Book: http://joshua.smcvt.edu/linearalgebra/book.pdf
Answer Key: http://joshua.smcvt.edu/linearalgebra/jhanswer.pdf

First write
$$
           1 = \frac{1}{2}\{(2x+1)-(2x-1)\} \\
           x = \frac{1}{4}\{(2x+1)+(2x-1)\} \\
           x^{2} = (x^{2}+x-1) - \frac{1}{4}\{(2x+1)+(2x-1)\}+\frac{1}{2}\{(2x+1)-(2x-1)\}
$$
Then you can easily write $ax^{2}+bx+c$ as a linear combination of $2x+1,2x-1,x^{2}+x-1$.
