(adsbygoogle = window.adsbygoogle || []).push({}); 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) [tex] q(x_1, x_2, x_3) = 4x_1x_2 - 2x_1x_3 + {x_2}^2 +2x_3x_2 [/tex]

[tex] x_1 = y_1 [/tex]

[tex] x_2 = -y_1 + y_2 + 2y_3 [/tex]

[tex] x_3 = -y_1 + 2y_2 + 2y_3 [/tex]

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

[tex] x_1 = y_1 [/tex]

[tex] x_2 = -y_1 + y_2 + 2y_3 [/tex]

[tex] x_3 = -y_1 + 2y_2 + 2y_3 [/tex]

?

From doing this PY=Xto get P?

And then I can do the whole Y^{T}P^{T}APY thing and get the matrix it's asking for?

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Quadratic Form and matrices question

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**