Question

The objective is to find the eigenvalues and corresponding eigenvectors. [2 0-1 1 Consider the matrix, A= 0 0 2 1 0 4

Answer 1

We have to find eigen values, and corresponding eigen vectors for the matrani A 2 12 0 4 Characteristie equation - 1 1 -> 0 2-) 6 4-> (2-x) ( 22 - x) (4-X). 1 (A - £) =0 -> - *3 +212-12.) + 2 = 0 2x3 – 13x² + 24 - 9 0 = (1-_) (212–1 21 +18) = 0 =) (x - 2) (x-3) (7-3) =0 eigen realues are : 1,= Ź, d2= 3. be eigen vector w. r. to x1 = 1 iel N2 let 3/2 2 X2 0 0 T H2 2x1- tuzo 3x - 282 -0. KI El 0-0 xz

w ht 42 43 be eigen veetar with respect to eigen realue d23 - 1 0 - 1 0 -5/2 .O 42 1, 0 41 f4 20 4 - Y 7 4 7 % =0 ka yo 42 Yz 2 B 0 (81