Answer
The set of polynomials are linearly independent
Work Step by Step
Step 1:
Write the coordinate vectors of the polynomials, produced by the coordinate mapping, that is:
(1 0 0 2), (2 1 -3 0), (0 -1 2 -1).
Step 2:
Write the coordinate vectors as a matrix and check for linear dependency (Ax=0)
\begin{bmatrix}
1 & 2 & 0 \\
0 & 1 & -1 \\
0 & -3 & 2 \\
2 & 0 & -1
\end{bmatrix}
$\Leftrightarrow$
\begin{bmatrix}
1 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 0
\end{bmatrix}
$\implies$ Since there is a pivot position in every column, the columns are independent and therefore also the corresponding polynomials.
