Question

Consider the matrix: 15 9 13 2 6 10 14 3 7 11 15 4 8 12 16 a- Find the eigenvectors of this matrix and their corresponding eigenvalues. b-Indicate if there are any degeneracy, and if so, change only one element of this matrix to remove this degeneracy (of course you need to recompute the eigenvalues to show that the degeneracy was lifted). Write a Mathematica program to calculate the roots of the following function f(x) = 0.5*e*-5*x+2 using two of the following numerical methods: a- Bisection method b- Secant method c- Newton method

Answer 1

a) 0 13 6-3 10 15 16-2 13 6-λ 1-2 5 3 4, 816-2 16-ג 2 (qu-al-120) + (-い(48-32)-เ-) +14 (24-28)

/2 [('-*)(90-15a-981. 5130-41) t13 (14-18 +3ג(:0 34 ± | (34,-4 ,(-80) 34 ± 38.4 34-38-4 2. 人0 -He eigenvectors are o,o,-a .2, 3b.2

6)to checn the deqenerocq , we haue to theck tshether -the deter- LO 4 8 16 13 13 2b y t53 15 4 8/b 9| 2 (112-120) _ bl48-60) + 14(24-28) |-10 | 11 I! 2-120)-5148-66) + 3248)I) (32-5b) + 13(6-2u) 2/90 -48)- 5 130-42) + ! 3 (N-18) -1t +1 2 +562-10-8+60-sajt. " -16+120-104-121-8+60-52 -9172-