Question

Problem TWO -3 1 1 0 0 Find the eigenvalues and the corresponding eigenvectors of the matrix | 0 1 0] Problem THREE

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Answer 1

find flee de ferrainant Find the cigan values, and the corresponding eigan vectors of the Beatrica 3 10 Corporate Slubion Given materia -3 lol fi O دارد۱ : And I 1 3 11 Co 0 O 10 : w T 0 0 0 (-3-1 in -d -d | Adil -3-4 ad D o ad 0 Now we expand along the along the row 2. 27 21-1-3 (-1) (-1) 0 1 => [ay]t" // <1/46-436,09 tot **** +0.t

a zyz Madrid - late ic 1 pow. we tale d=-3. =) -|-+3 The determinant at is ad-tc d-3 -x (Ed-3)(x) - (1.0) - - A CA+ 3)) =-d(+²+3d 14-1) -d? (173) This is the clovackeristie poly mrowd solue thee ecuation -d2C++3) -d220 i ta3 =0 te=0 ; 3=0 4:23 These are thee eigen pexh find flee eigen nectors -1 valer. -1-3 -3 1 0 A +3-3 1 0 3 3

3 w perform Pow operations to obtain flee erref at the matrie Make zeros im column 2 row I, coleum al except the entry R₂ = R₂ - (3) R1 o O 0. -3 : 3 R3= R3-R1 ) © 0 0 0 2 Now (R33 R3+ (2/2) R2 tol O

the rref at the solue We welis. Outro pora 0 19, 0 so IN 0 U NI If we heue no, al V3 NI2 - 0), There for ti 61 V? -0 0 ) d=0 -d-3 I 1 -d o ord o -3 lo 0 1 0 to obtain suolfenado yow perform - 3 0 0 0

-3 O V2:0, 02-H. Swap row (2 and & thee 0 -113 C o ecuation matrix solue. we pow 0 ve 0 o ne 0 V3 0 o €/3 If we face uz = t vir . Theme fone : اسا 12 V- o P 4.0 from eaua valies, ..-30 eigen eigen vector lov Thank your