Question

Find the characteristic equation of A, the eigenvalues of A, and a basis for the eigenspace corresponding to each eigenvalue. -5 14 A= 011 003 (a) the characteristic equation of A (b) the eigenvalues of A (Enter your answers from smallest to largest.) (14, 12, 23) = (c) a basis for the eigenspace corresponding to each eigenvalue basis for the eigenspace of 24 = basis for the eigenspace of 22 - basis for the eigenspace of 33 -

Answer 1

(a). The characteristic equation is A - 17 = 0 That is (-5 – 1) (1 - 1) (3 – 1) = 0 Therefore, the characteristic equation is A - X1 = 0 That is – 13 – 12 +171 – 15 = 0 (b). Therefore, the eigen values are -5, 1, 3. ? - (c). If ; is a given eigen value, then an eigen vector corresponding to ; is a non-zero solution vector of the linear system (A - \;I)X = 7 Therefore, we get u = (1,0,0), v = (9,8,16), w = (1,6,0)T as eigen vectors corresponding to the eigen values -5, 1, 3 respectively. Therefore, A basis for the eigen space of 11 = -5 is B1 {(1,0,0"} A basis for the eigen space of 12 = 1 is B2 = {(9,8, 16)"} A basis for the eigen space of 13 = 3 is B3 = {(1,6,0)"}