Question

) Let A be the following matrix: 13 0 2 0 2 2 0 0 6 (a) Enter its characteristic equation below. Note you must use p as the parameter instead of , and you must enter your answer as a equation, with the equals sign. (b) Enter the eigenvalues of the matrix, including any repetition. For example 16,16,24. 5 (c) Find the eigenvectors, and then use Gram-Schmidt to find an orthonormal basis for each eigenvalue's eigenspace. Build an orthogonal matrix whose columns are these eigenvectors. Enter this matrix, as a list of row vectors, below. (1 2 3 For example the matrix 4 5 6 would be entered as [1,2,3],[4,5,6],[7,8,9]. ( 7 8 9 (d) Enter the diagonal matrix P/ AP for your matrix P.

Answer 1

Please find the answer in the attached screenshot

1 302 Alo2o ac p is the parameter. nello. l 3-P o 2 l 2- po lao 4p+ (2-1)(3-7) (6-0-8 To o 6pl to the characteristic Equation is 4pt (2.p) (3-p) (6-p)-8 - Up+ (6 + pe=50 (6-0)-8 & 40+ 36+6p2_30p - 6p-p²+ sp²-8-0. 40 - p3 + 11p2 - 320 +28 -0. e p3-11p2 + 32p-28=0. Rooks are p= 2,2,7. so the Cigen values are po 2, 2,7 a) p22 (1027 yos, (3-2 0 2 oz 1 Lo 2-2 o lo oonloo a luzat, (2 0 6-2) 12ou loool vazt (-2 -261 ro C + Z b) D-7. 16272 1 3-7 o 27 4027 10-17 o 2-7012 L2 o 6-7 I 1201 looo- let usat ,viz t V₂ eo v Vz lot

so eigen vector's Coio].[-2,0, 1] [2107 P ro-2 1/27 ( 2 o o7 ТРАр 020 Plagonal matrix :