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Math Help - matrix determinants

  1. #1
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    matrix determinants

    I am real confused on determants. There is a couple examples below and if someone could show me how this is done that would be great.

    Find the determinant for this matrix:
    example 1)
    2 9 -5 3 9
    3 1 5 -3 1
    0 -4 1 2 -4
    8 5 6 9 5
    3 -2 -1 -3 -2

    example 2)
    3 0 0 0
    1 -2 0 0
    4 2 -1 0
    3 7 2 4
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by luckyc1423
    I am real confused on determants. There is a couple examples below and if someone could show me how this is done that would be great.

    Find the determinant for this matrix:
    example 1)
    2 9 -5 3 9
    3 1 5 -3 1
    0 -4 1 2 -4
    8 5 6 9 5
    3 -2 -1 -3 -2

    example 2)
    3 0 0 0
    1 -2 0 0
    4 2 -1 0
    3 7 2 4
    Second one is simple.
    Expand it along the first row
    You will get
    3 multipied by
    -2 0 0
    2 -1 0
    7 2 4
    Again expand it along the first row
    You wil get
    6 multiplied by
    -1 0
    2 4
    Hence determinant of the matrix comes out to be -24.

    Keep Smiling
    Malay
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  3. #3
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    Hello, luckyc1423!

    I am real confused on determants. There are a couple examples below
    and if someone could show me how this is done that would be great.

    If you're really confused and know nothing about determinants,
    . . you shoud not be playing by 4\times4 and 5\times5 determinants.

    If you're waiting for someone to work out the 5x5 for you,
    . . you may have a long wait.

    Having said that, I must assume that you know the general procedure.
    [If you don't, this is a total waste of time!]


    2)\;\;\begin{vmatrix}3&0&0&0\\1&\text{-}2&0&0\\4&2&\text{-}1&0\\3&7&2&4\end{vmatrix}

    As Malay pointed out, using the top row is best choice.

    . . . . . . . . + . - . .+ .-
    We have: / \begin{vmatrix}3&0&0&0\\1&\text{-}2&0&0\\4&2&\text{-}1&0\\3&7&2&4\end{vmatrix}

    . . = \;3\cdot\begin{vmatrix}\text{-}2&0&0\\2&\text{-}1&0\\7&2&4\end{vmatrix} - 0\cdot\begin{vmatrix}1&0&0\\4&\text{-}1&0\\3&2&4\end{vmatrix} + 0\cdot\begin{vmatrix}1&\text{-}2&0\\4&2&0\\3&7&4\end{vmatrix} - 0\cdot\begin{vmatrix}1&\text{-}2&0\\4&2&\text{-}1\\3&7&2\end{vmatrix}

    . . . . . . . . . . . . . . . . . + . - . +
    All we have left is: . 3\cdot\begin{vmatrix}\text{-}2&0&0\\2&\text{-}1&0\\7&2&4\end{vmatrix}

    . . = \;3\left[-2\cdot\begin{vmatrix}\text{-}1&0\\2&4\end{vmatrix} - 0\cdot\begin{vmatrix}2&0\\7&4\end{vmatrix} + 0\cdot\begin{vmatrix}2&\text{-}1\\7&2\end{vmatrix}\right]

    . . = \;3(-2)\cdot\begin{vmatrix}\text{-}1&0\\2&4\end{vmatrix}

    . . = \;-6\left[(-1)(4) - (0)(2)\right] \;= \;-6(-4 - 0) \;= \;-6(-4) \;= \;\boxed{24}

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  4. #4
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    so you could use this form of find determinents for every matrix?
    I did an example and could you tell me if im on the right track and if this is right......


    + - +
    2 5 -2
    3 1 2
    -1 -2 4


    = 2 * 1 2 - 5 * 3 2 + -2 * 3 1
    -2 4 -1 4 -1 -2

    = 2(4 + 4) - 5*(12 + 2) + (-2) *(-6 + 1)

    = 16 - 70 + 10

    = -44
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  5. #5
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    Hello, luckyc1423!

    so you could use this form of find determinents for every matrix? . . . Yes!

    I did an example and could you tell me if im on the right track and if this is right?

    .+ . .- . +
    \begin{vmatrix}2&5&\text{-}2 \\ 3&1&2\\\text{-}1&\text{-}2&4\end{vmatrix}

    = \;2\cdot\begin{vmatrix}1&2\\\text{-}2&4\end{vmatrix} - 5\cdot\begin{vmatrix}3&2\\ \text{-}1&4\end{vmatrix} - 2\cdot\begin{vmatrix}3&1\\ \text{-}1&\text{-}2\end{vmatrix}

    = \;2(4 + 4) - 5*12 + 2) + (-2)(-6 + 1)

    = \;16 - 70 + 10

    = \;-44

    Absolutely correct!
    . . . Nice work!

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  6. #6
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    Thanks that helped out a bunch! I just wish my teacher could have explained it as well as you did. Once again, thanks!
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  7. #7
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    Quote Originally Posted by luckyc1423
    Find the determinant for this matrix:
    example 1)
    2 9 -5 3 9
    3 1 5 -3 1
    0 -4 1 2 -4
    8 5 6 9 5
    3 -2 -1 -3 -2
    For this one, you're supposed to use a property of determinants instead of expanding it. Notice that the second and fifth columns are the same. That implies the determinant is zero.
    Last edited by JakeD; July 11th 2006 at 02:50 PM.
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  8. #8
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    Hello, JakeD!

    Notice that the second and fifth columns are the same.
    That implies the determinant is zero.

    Good eye, Jake!
    I was trying row operations, but missed that completely . . . *blush*
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