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Math Help - Matrix expansion

  1. #1
    Junior Member Greymalkin's Avatar
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    Matrix expansion

    Not sure how to input matrices into latex but its an easy problem:

    A=
    |7 -4 -6 |
    |2 0 -3 |
    |1 2 -5 |

    Evaluate |A| by expanding down the third column:
    I get:
    [-6(-1)4(3)]+[-3(-1)5(18)]+[-5(-1)6(8)]
    =-6(3)+3(18)-5(8)
    =-4

    answer is supposed to be -10, which i've arrived at expanding another row and column, what am I doing wrong?
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  2. #2
    MHF Contributor

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    Re: Matrix expansion

    Quote Originally Posted by Greymalkin View Post
    Not sure how to input matrices into latex but its an easy problem:

    A=
    |7 -4 -6 |
    |2 0 -3 |
    |1 2 -5 | Evaluate |A| by expanding down the third column:
    -6(4)+3(18)-5(8)=-10
    Thanks from Greymalkin
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  3. #3
    Junior Member Greymalkin's Avatar
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    Re: Matrix expansion

    ahh silly mistake 1x0, thank you very much sir!
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  4. #4
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    Re: Matrix expansion

    Quote Originally Posted by Greymalkin View Post
    Not sure how to input matrices into latex but its an easy problem:

    A=
    |7 -4 -6 |
    |2 0 -3 |
    |1 2 -5 |

    Evaluate |A| by expanding down the third column:
    I get:
    [-6(-1)4(3)]
    How did you get "3" here? 6\left|\begin{array}{cc}2 & 0 \\ 1 & 2\end{array}\right|= 6(4)

    +[-3(-1)5(18)]+[-5(-1)6(8)]
    =-6(3)+3(18)-5(8)
    =-4

    answer is supposed to be -10, which i've arrived at expanding another row and column, what am I doing wrong?
    Thanks from Greymalkin
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  5. #5
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    Re: Matrix expansion

    Hello, Greymalkin!

    A\:=\:\begin{vmatrix}7&\text{-}4&\text{-}6 \\2&0&\text{-}3 \\ 1&2&\text{-}5\end{vmatrix}

    \text{Evaluate }|A|\text{ by expanding down the third column.}

    \text{I get: }\:[\text{-}6(\text{-}1)^4(3)]+[\text{-}3(\text{-}1)^5(18)]+[\text{-}5(\text{-}1)^6(8)] . Not sure what all this is.
    . . . =\;\text{-}6(3)+3(18)-5(8) \;=\;-4

    Answer is supposed to be -10, which i've arrived at expanding another row and column.
    What am I doing wrong?

    Down the third column . . .

    . . \text{-}6\begin{vmatrix}2&0\\1&2\end{vmatrix} - (\text{-}3)\begin{vmatrix}7&\text{-}4 \\ 1&2 \end{vmatrix} - 5 \begin{vmatrix}7 & \text{-}4 \\ 2 & 0 \end{vmatrix}

    . . =\;-6\underbrace{(4-0)}_{\text{Here!}} + 3(14 +4) - 5(0+8)

    . . =\;-24 + 54 - 40

    . . =\;-10
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