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the prof did it already but I dont understand how...here it is

You are given that L : R2 −> R2 is a linear map for which B =

{(1, 1), (1, 2)} is a basis of R2 consisting of eigenvectors of L with corresponding

eigenvalues 1/2 and 1 respectively – i.e. L(1, 1) = 1/2(1, 1) and

L(1, 2) = (1, 2).

c) Determine the coordinates of the vector (3, 5) with respect to the basis

B and determine the value of L^n (3, 5) as n tends to infinity

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Ok to find coordinates of that vector 3,5 its easy enough

[1 1 | 3 ]

[1 2 | 5 ]

and row reduce it to get

[1 0 | 1 ]

[0 1 | 2 ]

so (3,5)B = (1,2)

to determine L(3,5) I got 1/2(1,1) + 2(1,2)

now the prof said to determine L

**^n**(3,5) that equals (1/2)

**^n**(1,1) + 2(1,2)

why didnt he put the 2^n why do you put the 1/2^n only and NOT the 2 to the power of n??

I dont get how to get L^n (3,5)

HELPPP???????????????????????????????