# Power of a Matrix

• May 31st 2010, 09:52 AM
shannu82
Power of a Matrix
A = {[2 1 2 ] [2 1 2 ] [2 1 2 ]}^8
Compute the power matrix using the PDP^-1
I got the eigen values to be 1, 2.
i am having difficulty forming the vector and therefore continuing the question. Could anyone explain this?
• May 31st 2010, 12:42 PM
Opalg
Quote:

Originally Posted by shannu82
A = {[2 1 2 ] [2 1 2 ] [2 1 2 ]}^8
Compute the power matrix using the PDP^-1
I got the eigen values to be 1, 2.
i am having difficulty forming the vector and therefore continuing the question. Could anyone explain this?

Is that meant to mean that the three rows of A are all equal to 1 2 1? If so, the eigenvalues are 0 and 5, not 1 and 2. Please supply a correct version of the problem.
• Jun 1st 2010, 11:21 AM
shannu82
Quote:

Originally Posted by Opalg
Is that meant to mean that the three rows of A are all equal to 1 2 1? If so, the eigenvalues are 0 and 5, not 1 and 2. Please supply a correct version of the problem.

um the question actually looks like
[212]
[212]
[212]

That whole matrix to the power of 8.
• Jun 1st 2010, 12:01 PM
Opalg
Quote:

Originally Posted by shannu82
um the question actually looks like
[212]
[212]
[212]

That whole matrix to the power of 8.

Have you tried multiplying the matrix by itself to see what its square looks like? If so, did you notice that the square is exactly 5 times the original matrix? So what would happen if you squared the result again? And again?