Answer to Question #238795 in Linear Algebra for Parkavi

Question

Q=x1^2+3x2^2+3x3^2-2x2x3

Answer 1

$Q=(x_1)^2+3(x_2)^2+3(x_3)^2-2(x_2)(x_3)\\ Q=(x_1)^2+2(x_2)^2+2(x_3)^2+(x_2)^2+(x_3)^2-2(x_2)(x_3)\\ Q=(x_1)^2+2(x_2)^2+2(x_3)^2+(x_2-x_3)^2\\ Q= \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} \begin{bmatrix} x_1 & 2x_2 & 2x_3\\ \end{bmatrix} +\begin{bmatrix} x_2-x_3 \end{bmatrix}\begin{bmatrix} x_2-x_3 \end{bmatrix}$