Question

Given this matrix, write the Characteristic Equation, and the Eigenvalues with their proper eigenvectors

A = [ 17 21 2 4

Answer 1

A = 72] Page 1 To find characteristic squation, | A-20]=0 113:3-46938 al 7-> 2 2 4- (7-2)(4-2) – 4 =0 X-112+28 - 4 =0 X2_11x + 24 =0 characteristic squation characteristic sq. find the roots of 2 24*? ^ M?-89-32 +24 50 x(x-8) -3(x-8)=0 (21-3)(x-8)=0 2,=8 X2=3 Hence, The eigen values are di=8 d2=3

Next, find the eigen vectors, 2 Page 2 at x = 8 (A-XI) = (A - 81) (51)-(3) · 1)?:) row operations reduce the above matrix by Performing (R2 → R2+2R,) - 15:] ㄱ (P. — -R) -2 0 0 matrix Lauation, Now, solve the (A-21). ✓ (636)-(3) Let ₂=t Ui-24 =0 v=2t Therefore, VE (2)-1] a- at = 8, Eigen vector =

At x=3 (A-NE) - (A-32) Page 3 -:-) 4 2 i 2 How operations to obtain reduced matrix Perform, (R2 + R2 - RO) 4 2 0 O (R. - ) co 0 Now, solve the matrix qauation, (A-21) J (+(*) -(0) Let U₂=t V, t 1 q zo &i= - t Therefore, 190 vector Hence, at x=3 Eigen