4. Given matrix 3 (-²1) 0 5 4 -2 -14 B = -12 (a) Find the eigenvalue(s) of B. (b) Find the eigenvalue(s) of B². (c) What conclusion can you make by comparing answers from part (a) and (b)?

The matrix 10 -24 -24 -10 has eigenvalues 26 and -26, and corresponding eigenvectors (3,-2) 1 and (2,3) respectively, both of magnitude 1. √13 (a) Write down an orthogonal matrix P and a diagonal matrix D such that PT AP = D. A = 20 1 /13 (b) Use your answer to part (a) to find the standard form of the equation of the non-degenerate conic with equation 10.x² - 48ry - 10y² + 3x - 2y = 0. (c) Hence state whether the conic is an ellipse, a parabola or a hyperbola.

(a) (b) and (c) please

Please help me solve this. I got to all three eigens are equal to zero by doing subtraction of 5(first equation)-(third equation) and 3(first equation)-(second equation) and then solced out for my "a" "b" and "c" values. where did I go wrong here?? only HANDWRITTEN answer needed ( NOT TYPED)