Consider this matrix

**zet** · March 30th 2009, 09:48 PM

consider the matrix M= (2 0, 0 2)^n, for n>1 ; n E 1.

Calculate M^n for n= 1, 2, 3, 4, 5, 10, 20, 50. describe any pattern observed, and generalize the pattern into an expression for the matrix M^n in terms of n.

Determine detM for the powers of the matrices calculated above. Describe any pattern observed, generalize the pattern into an expression for det(M^n) in terms of n.

HELP please!>?.

Thanks in advance.
~Zet

**Showcase_22** · March 31st 2009, 04:26 AM

This might help:

$\begin{pmatrix} {2}&{0}\\ {0}&{2} \end{pmatrix}^n=2^n\begin{pmatrix} {1}&{0}\\ {0}&{1} \end{pmatrix}^n=\begin{pmatrix} {2^n}&{0}\\ {0}&{2^n} \end{pmatrix}$

As for the determinant:

$\begin{vmatrix} {2^n}&{0}\\ {0}&{2^n} \end{vmatrix}=(2^n)^2=2^{2n}$

**aidan** · March 31st 2009, 02:17 PM

Showcase_22, excellent reply.
That explained most of zet's question to me.

However,

Originally Posted by zet

... M= (2 0, 0 2)^n, for n>1 ; n E 1.

what does

n E 1

mean?

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