Question

solve them by clear hand write , thankyou
3. a) (7 pnts) Find all eigenvalues of the matrix A = 3 -5 3 16 -6 4 11 -3 3 b) (7 pnts) Find all eigenvectors of the matrix A = 13 -5 3 16 -6 4 -E c) (6 pnts) What can you say about the solution of the following system of differential equations in relation to the matrix A? Please explain briefly. X1 - 3x2 + 3x3 3x1 - 5x2 + 3x3 = 6x1 - 6x2 + 4x3 tz'

Answer 1

3.

Given matrix -3 A -5 3 6 4 -6. a for eigenvalues, first we find its chonacteristic equation I-a -3 3 3 -s-a - 6 - 6 4-a + 13 +02-122-16=0 (2+2)² (2-4) -O So, eigen values are. di= d2= -2 3 b eigenvactor corresponding to is [A-AI] ou d -2 3 - 3 3 1 3 -3 3 Ja :) CS Scanned with CamScabiner - 6

9 9 9 span - "{[:1:01 so eigenvactors corresponding to a=-2 are and 1 ] (10) eigenspace for 2-4 [A-41] Ñ = TO 3 -3 3 Si P2 3 - 9 3 P3 6 -6 -18] {{ :]} = ) li span l3 so eigenvactor for a=4 d. 2 Scanned with CS CamScanner

С Hence the solution of given system es given by n X2 cie"(!) *4.4.4(esence 3 CS Scanned with CamScanner