I just need help with #4. Had to include #3 since they are related Given the lin

Question

I just need help with #4. Had to include #3 since they are related

Given the linear transformation L : R3 rightarrow R3 = (x1 + x2, x1 + x2 + x3, x2 + x3)T, find the matrix representation of A for unit vector basis. Suppose this linear transformation governs the equation x n+1 = .Axn, and consider the new basis u1 = (1/2, - /2, 1/2)T, u2 = (- /2,0, /2)T, u3 = (1/2, /2, 1/2)T. What do you expect the long-time behavior of .A n ui, for each of the basiss u i, i = 1,2,3 as n rightarrow infinity ? Following the above question, find the similar matrix B for A under the basis U = [u1, u2, u3]. Based on the similar matrix. discuss the long time behavior of an arbitrary vector times in R3 when multiplied by An as n rightarrow infinity .

Explanation / Answer

this link will help you a lot

http://www.math.tamu.edu/~stecher/LinearAlgebraPdfFiles/exercisesChap3.pdf

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