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Please help me with this problem which must be solved using eigenvalues and eigenvectors:

A geometric sequence of vectors (2x1 row vectors) where to get from one term to the next multiply by a matrix (2x2):

t =(R^(n-1))*a

Where:

t is the nth vector in the sequence

R is the 2x2 matrix

R=

[a b]

[c d]

1.Does t converge as n->infinity? What conditions are sufficient for the sequence to converge? What vector does tn converge in each case?

2.What is the formula for the sum of the first n vecotrs in this sequence? Under what conditions and to what vectors does it converge

Thanks!

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# Problem involving eigenvalues/vectors

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