- #1
salman213
- 302
- 1
Hi I have a final comming up soon so I was looking at an older final and saw this question
the prof did it already but I don't 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 don't get how to get L^n (3,5)
HELPPP??
the prof did it already but I don't 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
--------------------------------------------------------------------
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 don't get how to get L^n (3,5)
HELPPP??