Show that any four polynomials in $P_2$ are linearly dependent

Question

[I attempted this question but just wanted to check if I'm on the right track.

I started the question by :

Let { ($a_o$+$a_1$$x^2$), ($a_o$-$a_1$$x^2$), ($a_1$$x^2$-$a_0$), ($a_1$$x^2$-$a_2$x) ∈ $P_2$

Followed by putting in vector form and into a matrix, reducing it to row echelon form and comparing the rank to the number of columns to determine it is lenearly dependent. Am I right to do it this way?