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Math Help - Matrix and vector multiplication

  1. #1
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    Matrix and vector multiplication

    Hello,
    Im trying to learn the rules for multiplying a row vector and matrix together, can anyone please tell me if Im right or wrong about:


     \begin{pmatrix} a& b & c\end{pmatrix} * \begin{pmatrix}e & f & g\\h & i & j\\ k & l & m\end{pmatrix} =  \begin{pmatrix} ae+ah+ak& bf+bi+bl & cg+cj+cm\end{pmatrix}
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  2. #2
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    Dear NotGoodAtMath94,

    Your multiplication of matrices is incorrect. The correct one is,

    \begin{pmatrix} a& b & c\end{pmatrix} * \begin{pmatrix}e & f & g\\h & i & j\\ k & l & m\end{pmatrix}<br />
= <br />
\begin{pmatrix} ae+bh+ck& af+bi+cl & ag+bj+cm\end{pmatrix}<br />

    Hope this will help you.
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  3. #3
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    Thank you for showing me
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  4. #4
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    Quote Originally Posted by NotGoodAtMath94 View Post
    Hello,
    Im trying to learn the rules for multiplying a row vector and matrix together, can anyone please tell me if Im right or wrong about:


     \begin{pmatrix} a& b & c\end{pmatrix} * \begin{pmatrix}e & f & g\\h & i & j\\ k & l & m\end{pmatrix} =  \begin{pmatrix} ae+ah+ak& bf+bi+bl & cg+cj+cm\end{pmatrix}
    Think of a matrix multiplication as a series of "dot products". The number at the "i,j" place in the product AB is the dot product of the ith row of A and the jth column of B.

    In your example, row 1 of A is (a, b, c) and column 1 of B is (e, h, k). The "dot product" of those is ae+ bh+ ck so your first number in the first column is ae+ by+ ck, not ae+ ah+ ak where you have multiplied the first column by a only.

    In this case, since A has only one row, the product has only one row.
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  5. #5
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    Hello, NotGoodAtMath94!

    \begin{pmatrix} a& b & c\end{pmatrix}* \begin{pmatrix}e & f & g\\h & i & j\\ k & l & m\end{pmatrix}

    We multiply the row vector by each column vector.


    The three multiplications are:

    . . \begin{pmatrix}a&b&c\end{pmatrix}*\begin{pmatrix}e  \\h\\k\end{pmatrix} \;=\;ae + bh + ck

    . . \begin{pmatrix}a&b&c\end{pmatrix} * \begin{pmatrix}f\\i\\l\end{pmatrix} \;=\;af + bi + cl

    . . \begin{pmatrix}a&b&c\end{pmatrix} * \begin{pmatrix}g\\j\\m\end{pmatrix} \;=\;ag + bj + cm


    Since (1\times3) * (3\times3) \;\to\;(1\times 3), the product is a (1\times 3) row vector:

    . . . . \begin{pmatrix}ae+bh+ck & af+bi+cl & ag+bj+cm \end{pmatrix}

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