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Math Help - Consider this matrix

  1. #1
    zet
    zet is offline
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    Consider this matrix

    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
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  2. #2
    Super Member Showcase_22's Avatar
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    This might help:

    \begin{pmatrix}<br />
{2}&{0}\\ <br />
{0}&{2}<br />
\end{pmatrix}^n=2^n\begin{pmatrix}<br />
{1}&{0}\\ <br />
{0}&{1}<br />
\end{pmatrix}^n=\begin{pmatrix}<br />
{2^n}&{0}\\ <br />
{0}&{2^n}<br />
\end{pmatrix}

    As for the determinant:

    \begin{vmatrix}<br />
{2^n}&{0}\\ <br />
{0}&{2^n}<br />
\end{vmatrix}=(2^n)^2=2^{2n}
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  3. #3
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    Showcase_22, excellent reply.
    That explained most of zet's question to me.

    However,
    Quote Originally Posted by zet View Post
    ... M= (2 0, 0 2)^n, for n>1 ; n E 1.
    what does
    n E 1
    mean?
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