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Math Help - Matrix Multiplication

  1. #1
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    Matrix Multiplication

    Hello,

    What is the product of the following two matrices? In my book, the answer is A, while I believe it is B because if c1 = r2 , then a product exists. However, this is not upheld in this given question because c1 = 1, and r2= 4.
    Here is the problem:
    The product of (-2 -1 5 9) (0 -5)
    (3 -2)
    (4 0)
    (-7 1) is:

    Answers~
    A) (-37)
    (21)
    B) product is not defined
    The other choices are irrelevant to my question.
    Thank you for the help, it is greatly appreciated.
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  2. #2
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    Re: Matrix Multiplication

    Hello, pepelepew23!

    What is the product of the following two matrices?

    . . \begin{pmatrix}\text{-}2 & \text{-}1 & 5 & 9 \end{pmatrix}\begin{pmatrix}0 & \text{-}5 \\ 3 & \text{-}2 \\ 4 & 0 \\ \text{-}7 & 1 \end{pmatrix}

    . . (A)\;\begin{pmatrix}\text{-}37 \\ 21 \end{pmatrix}\qquad (B)\;\text{product is not defined.}

    The other choices are irrelevant to my question. . Really?

    In my book, the answer is A, while I believe it is B
    . . because if c1 = r2 , then a product exists.
    However, this is not upheld in this given question because c1 = 1, and r2= 4.
    Not true . . . The first matrix has four columns: c1 = 4.

    We are multiplying a 1\!\times\!4 matrix by a 4\!\times\!2 matrix.
    The product is a 1\!\times\!2 matrix . . . That's one row and two columns: . \begin{pmatrix}* & * \end{pmatrix}
    The book's answer is wrong; it is a 2\!\times\!1 matrix . . . the wrong shape!

    \begin{pmatrix}\text{-}2 & \text{-}1 & 5 & 9 \end{pmatrix}\begin{pmatrix}0 & \text{-}5 \\ 3 & \text{-}2 \\ 4 & 0 \\ \text{-}7 & 1 \end{pmatrix}

    . . =\;\bigg((\text{-}2)(0) + (\text{-}1)(3) + (5)(4) + (9)(\text{-}7),\;(\text{-}2)(\text{-}5) + (\text{-}1)(\text{-}2) + (5)(0) + (9)(1)\bigg)

    . . =\;\(0-3+20-63,\:10 + 2 + 0 + 9)

    . . =\;(\text{-}46,\:21)
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