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Math Help - Determinant

  1. #1
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    Determinant

    Hello.

    I'm asked to find the value of the following determinant using cramer's rule.

    0 , 1 , 2
    4, -5 , 8
    8, 0 , -9


    so I repeat the first two columns


    0 1 2 0 1
    4 -5 8 4 -5
    8 0 -9 8 0


    and then I multiply diagonally and add and then subtract and I get


    0+64+0- -80+0-36=
    64 +80-36 = 108

    so My answer is 108, but all calculators tell me that my answer should be 180, why? I suspect that I should be adding 36 in that case I would get 180, but I don't see how I could be adding 36 if 36 has a negative sign. please help me.
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  2. #2
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    Quote Originally Posted by jhonwashington View Post
    Hello.

    I'm asked to find the value of the following determinant using cramer's rule.

    0 , 1 , 2
    4, -5 , 8
    8, 0 , -9


    so I repeat the first two columns


    0 1 2 0 1
    4 -5 8 4 -5
    8 0 -9 8 0


    and then I multiply diagonally and add and then subtract and I get


    0+64+0- (-80+0-36)=
    64 +80-36 = 108

    so My answer is 108, but all calculators tell me that my answer should be 180, why? I suspect that I should be adding 36 in that case I would get 180, but I don't see how I could be adding 36 if 36 has a negative sign. please help me.
    Hello,

    you've forgotten to use brackets. I've added them in the quoted text.
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  3. #3
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    Hello, jhonwashington!

    You made a teensy error . . .


    Evaluate the determinant: . \begin{vmatrix}\: 0 & 1 & 2\: \\ \:4 & \text{-}5 & 8\: \\ \:8 & 0 & \text{-}9\:\end{vmatrix}


    So I repeat the first two columns: . \begin{array}{ccccc}0 & 1 & 2 & 0 & 1 \\<br />
4 & \text{-}5 & 8 & 4 & \text{-}5 \\<br />
8 & 0 & \text{-}9 & 8 & 0 \end{array}


    and then I multiply diagonally and add and then subtract and I get:

    . . 0 + 64 + 0  - 80 + 0 \underbrace{-36}_{{\color{blue}\text{Here!}}}

    Multiply diagonally: . \underbrace{(0)(\text{-}5)(\text{-}9)}_{+0} + \underbrace{(1)(8)(8)}_{+64} + \underbrace{(2)(4)(0)}_{+0} \underbrace{- (2)(\text{-}5)(8)}_{+80} - \underbrace{(0)(8)(0)}_0 \underbrace{- (1)(4)(\text{-}9)}_{{\color{red}+36}}


    And we get: . 0 + 64 + 0 + 80 - 0 + 36 \;=\;\boxed{180}

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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by jhonwashington View Post
    I'm asked to find the value of the following determinant using cramer's rule.
    Am I missing something? I thought Cramer's rule was used to find the solution to a system of equations, not to find determinants?

    -Dan
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