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, set up the matrix so that every row is a vector. eg,
$$
\begin{bmatrix}x^2 & x & -1 \\0 & 2x & 1 \\ 0 & 2x & -1 \end{bmatrix}
$$
if you want to, you can simply represent the variables in a "normalized" basis by simply deciding that $\bar b_1 = x^2$. You can now use a "change of basis" from $\bar b_n$ to $\bar e_n$.
Then, row reduce and determine the linear independence.  
