Question

Determine the largest eigenvalue of the 3 x 3 matrix 281 309 001 O a. 1 06.6 OC.A Od.2 QUESTION 2 Determine the larger eigenvalue of the linear transformation T(x,y) = (2x + 3y . x + 4y) O a.5 Ob.2 O c. 1 Od.4

please answer all three questions
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Answer 1

Question 1 Let A = mo oooo -o- The characteristic polynomial of from the determinant of (A-AI). a in obtained 2- 8 (1) ((2-2) (-4) - 24) (1-x) = -2 -24) - (1-2) (-6) (+4) the roots of the The eigen values of A are characteristic polynomial of A Hence the eigen values of A are obtained from (1) (-6) (4+4) = 0 >> 121,-4,6. Honce the largest eigen rate of A be O b. [6] Guestion 2 : T (ny) = (20 ty, a. Let B be the standard basis. Then the matrix representation of T with respect to B be

let B- [ 3 ] . The charcteristic polynomial of B be (2-2) (4-1) - 3. 2 8-61+1 -3. & bits The roots of the charcteristic polynomial of B be ď - 61+5 =0 x-strats=0 ..125,1. Hence the eigen values of B are 5 and 1. . The largest eigenvalue of the linear Transfor- mation be O a. 5 Question - 3. The eigen values of c- [ obtained from the equation. ] (say is (1-1) (3-2) + 120 - 41+4=0 = 2,2

The respeated eigen value ke 2 net x be a vector such that [A-xI] x = 0, where a=2. let x= (y) . - 4 th = 0 24 = . ..Xam ). with the Hence an eigen rector repeated eigen vale a associated a be of ob

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