Answer to Question #328190 in Linear Algebra for peac_eboy

Question

QUESTION 4 Find the quadratic form q(X) that corresponds to the symmetric matrix

𝐴 = [ 1 2 3 2 − 1 2 3 2 − 1] ( is 3by3 matrix)

Answer 1

$A=\left[ \begin{matrix} 1& 2& 3\\ 2& -1& 2\\ 3& 2& -1\\\end{matrix} \right] \\q\left( x \right) ={x_1}^2-{x_2}^2-{x_3}^2+2\cdot 2x_1x_2+2\cdot 3x_1x_3+2\cdot 2x_2x_3=\\={x_1}^2-{x_2}^2-{x_3}^2+4x_1x_2+6x_1x_3+4x_2x_3$