MathCastle
Linear AlgebraEasySymmetric Matrices & Quadratic Forms

Symmetric Matrices & Quadratic Forms · Easy problem

A quadratic form q(x)=xTAxq(\mathbf x) = \mathbf x^{T}A\mathbf x on R2\mathbb R^2 is diagonalized by an orthogonal change of variables x=Qy\mathbf x = Q\mathbf y, giving q=2y12−5y22q = 2y_1^2 - 5y_2^2. Find the value of qq at the point whose new coordinates are y=(3,1)\mathbf y = (3, 1).