Question

Find the matrix A of the quadratic form associated with the equation. 6x2 - 9xy - 6y2 + 5 = 0 A= Find the eigenvalues of A. (Enter your answers as a comma-separated list.) 2 = Find an orthogonal matrix P such that PTAP is diagonal. (Enter the matrix in the form [[row 1], [row 2], ...), where each row is a comma-separated list.) P = Need Help? Read It Talk to a Tutor

Answer 1

Given quadratric form 6x² - xy - by² +6=0 This can be written in matrix form (w s] [](3) [_(%) *'s-o А 6 - 9/2 .] -ah Eigen values 111-A1:0 -9/2 -9/2 - 6 9/2 > 9/2 x+6 (4-6) (2+5) 81 -0 2-36 -81 -0 ) 36481 . +7.5 Eigen values of * are 7.5, -as

To find pin PTAP -a/2 -6 -al O R2 - Rret. & + 3 R 6 -a/2 22 3ly ca at 24 -32 314 O 3ly 1 P = [6 p= 314 We can check P'AP 1 -6 314 I 6-92 -9/2-6 6 -9/2 3ly JC: 9/2-9/ .27 8

which is a ؛ diagonal matrix " [.. و3