3.a.Given the linear transformation L : R3 ? R3 = (x1 + x2,x1 + x2 + x3,x2 + x3)

Question

3.a.Given the linear transformation L : R3 ? R3 = (x1 + x2,x1 + x2 + x3,x2 + x3)T , find the matrix representation of A for unit vector basis.

b.Suppose this linear transformation governs the equation X(n+1) = Axn,and consider the new basis u1= (1/2, -?2/2, 1/2)T, u2= (-?2/2,0,?2/2)T, u3= (1/2, ?2/2, 1/2)T. What do you expect the long-time behavior ofA^n(ui)for each of the basis ui

; i = 1,2,3 as n apporaches infinity.

4.a) Following the above question, find the similar matrix B for A under the basis U = [u1; u2; u3]

b.b) Based on the similar matrix, discuss the long time behavior of an arbitrary vector x in R3 when multipliedby A^n as n approaches infinity.

(I only need help for question 4 so question 3 was added because question 4 follows 3)

Explanation / Answer

you want complete solution or just answer reply fast

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.