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Math Help - Matrix

  1. #1
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    Matrix

    A=\begin{vmatrix}<br />
  1 & 0&0 \\<br />
  3& \omega &0\\<br />
0&3-i&\omega^2<br />
\end{vmatrix}\\

    where i is iota and w is cube root of unity.

    Find

    1) A^{105}

    2) A^{106}

    3) A^{108}

    4) A^{109}
    Last edited by mr fantastic; March 29th 2010 at 03:39 AM. Reason: Fixed latex. And aded information from a duplicate post.
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  2. #2
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    Quote Originally Posted by banku12 View Post
    A=\begin{vmatrix}<br />
1 & 0&0 \\<br />
3& \omega &0\\<br />
0&3-i&\omega^2<br />
\end{vmatrix}\\

    then ..find



    1) A^{105}
    2) A^{106}
    3) A^{108}
    4) A^{109}
    You need to diagonalise A to find these higher powers of A

    Read this Diagonalization
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  3. #3
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    Quote Originally Posted by pickslides View Post
    You need to diagonalise A to find these higher powers of A

    Read this Diagonalization
    ok thanks

    but can u jus solve the first one for me.....it wud help me in doing rest

    i will solve rest by myself....plz do the first one

    btw it went abov my head

    if suppose i need to find the trace of the higher powers do i hav to follow that method only or der is some other way also
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  4. #4
    Super Member Bacterius's Avatar
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    Quote Originally Posted by banku12 View Post
    ok thanks

    but can u jus solve the first one for me.....it wud help me in doing rest

    i will solve rest by myself....plz do the first one

    btw it went abov my head

    if suppose i need to find the trace of the higher powers do i hav to follow that method only or der is some other way also
    You really should read the text proposed by Pickslides. It will help you a lot more than just looking at a mysterious example.
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  5. #5
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    mr fantastic's Avatar
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    Quote Originally Posted by banku12 View Post
    A=\begin{vmatrix}<br />
1 & 0&0 \\<br />
3& \omega &0\\<br />
0&3-i&\omega^2<br />
\end{vmatrix}\\

    where i is iota and w is cube root of unity.

    Find

    1) A^{105}

    2) A^{106}

    3) A^{108}

    4) A^{109}
    Is A meant to be the determinant (that's what the notation you've used means)? If so, the questions are trivial (since the matrix is lower triangular) ....
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  6. #6
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    ya its a MATRIX

    sorry its looking lik a determinant in fig

    Quote Originally Posted by Bacterius View Post
    You really should read the text proposed by Pickslides. It will help you a lot more than just looking at a mysterious example.
    i din understand that stuff...thats why asking to give the soln for first
    Last edited by mr fantastic; March 29th 2010 at 03:59 AM. Reason: Merged posts
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