Homework Help: Quadratic Form and matrices question

1. Feb 20, 2010

zeion

1. The problem statement, all variables and given/known data

Find the matrix that represents the given quadratic form relative to the variables yi.
a) $$q(x_1, x_2, x_3) = 4x_1x_2 - 2x_1x_3 + {x_2}^2 +2x_3x_2$$

$$x_1 = y_1$$
$$x_2 = -y_1 + y_2 + 2y_3$$
$$x_3 = -y_1 + 2y_2 + 2y_3$$

2. Relevant equations

3. The attempt at a solution

Can I get the change of basis matrix P from B to standard R3 basis from this stuff

$$x_1 = y_1$$
$$x_2 = -y_1 + y_2 + 2y_3$$
$$x_3 = -y_1 + 2y_2 + 2y_3$$

?

From doing this PY = X to get P?

And then I can do the whole YTPTAPY thing and get the matrix it's asking for?