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Math Help - Matrix problems

  1. #1
    Newbie
    Joined
    Dec 2010
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    Matrix problems

    1) Find the matrix product, if possible, please.
    [ 6 0 -4 ] [1]
    [ 1 2 5 ] [2]
    [ 10 -1 3] [3]

    2) Decide whether the given matrices are inverse of each other. ( Check to see if their product is the identity matrix 1:

    [ 1 0 0 ] [1 0 0]
    [ -1 -2 3 ] and [ 0 0 1]
    [ 0 1 0] [1/3 1/3 2/3]

    Thank you!
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  2. #2
    Super Member

    Joined
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    Lexington, MA (USA)
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    Hello, Mathgirl7!

    Exactly where is your difficulty?
    If you don't know matrix multiplcation,
    . . very few of us are willing to teach it here.


    \text{1) Find the matrix product, if possible.}

    . . \begin{pmatrix} 6 & 0 &\text{-}4 \\ 1 & 2 & 5 \\ 10 & \text{-}1 & 3 \end{pmatrix}  \begin{pmatrix}1 \\ 2 \\ 3 \end{pmatrix}
    \text{Answer: }\;\begin{pmatrix}\text{-}6 \\ 15 \\ 17 \end{pmatrix}



    \text{ 2) Decide whether the given matrices are inverses of each other.}
    . . . \text{(Check to see if their product is the identity matrix }I.)

    . . \begin{pmatrix}1 & 0 & 0 \\ \text{-}1 & \text{-}2 & 3 \\ 0 & 1 & 0 \end{pmatrix} \begin{pmatrix}1 & 0 & 0 \\ 0 & 0 & 1 \\ \frac{1}{3} & \frac{1}{3} & \frac{2}{3} \end{pmatrix}

    Yes, they are inverses of each other.

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