Please Show your work Consider the difference equation xk+1-Axk where A has eige

Question

Please Show your work

Consider the difference equation xk+1-Axk where A has eigenvalues and corresponding eigenvectors vi, v2, and v3 below. Find the general solution of this difference equation if xo is given as below. gi What is xk as k--> infinity? What is A? Find Ak ven 48) A) xk = 5(1)kv1-3(0.8)kv2 + (0.6)kv3 O xk(+(0.8v2+(0.6)v B) xk 1(1)kvI + 1(0.8)kv2 2(0.6)kv3 D) xk (1) v1 3(0.8) v2+3(0.6) v3 10 -10 49) 20 -33 A) xk = 4(1)kv1-4(07)kv2 + (0.5)kv3 O xk-(D+ (0.7*v2+(0.5)kvs B) xk (1) 1-4(0.7 v2 -60.5)kv3 D) xk--2)v 1(0.7 v2+1(0.5) v3 0 50) A) xk- 2(3)kv1-1(0.9)kv2-2(0.5)kv3 C) xk = 4(3)kv1-4(0.9)kv2 + (0.5)kv3 B) xk- (3)kv1 4(0.9) v2-3(0.5)kv3 Compute the dot product u v 51) 17 A) 14 B) 22 C) 53 D) 20 52 2 52) A) 2 B)-8 C) 8 D) 0 10 2 53) u=1 ?? 3 53) A) 18 B) 0 C) 15 D) 25 10

Explanation / Answer

51)

u.v=(1)(3)+(17)(1)=3+17=20

52)

u.v=(-1)(3)+(5)(2)+(3)(-5)=-3+10-15=-8

53)

u.v=(10)(2)+(0)(3)+(5)(-1)=20-5=15

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