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Math Help - Adding and Subtracting Matrices

  1. #1
    Nov 2011

    Adding and Subtracting Matrices

    I've got this problem from my SAT Math level 2 prep book, which I think has the wrong answer.

    The question is: Adding and Subtracting Matrices-img-20111108-00174.jpg

    So what I did was subtract the matrix on the right by the left, and then both multiply both sides by -1.

    The answer I get is
    (-4 1 -11)
    8 -1 -2

    However in the book, the answer says b)Adding and Subtracting Matrices-img-20111108-00175.jpgAdding and Subtracting Matrices-img-20111108-00176.jpg

    I have never done matrices before reading this book, and I'm trying to learn from the book. This is proving difficult as this book is quite hard to read, although I correctly answered the previous questions.
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  2. #2
    Super Member

    May 2006
    Lexington, MA (USA)

    Re: Adding and Subtracting Matrices

    Hello, fobbz!

    Solve for X:\;\;\begin{pmatrix} 1&2&3 \\ 2&1&3\end{pmatrix} - X \;=\;\begin{pmatrix}5&1&8 \\ \text{-}6&0&5\end{pmatrix}

    We have: . X \;=\;\begin{pmatrix} 1&2&3 \\ 2&1&3\end{pmatrix} - \begin{pmatrix} 5&1&8\\ \text{-}6&0&5\end{pmatrix}

    Therefore: . X \;=\;\begin{pmatrix}\text{-}4 & 1 & \text{-}5 \\ 8 & 1 & \text{-}2\end{pmatrix}

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  3. #3
    MHF Contributor

    Mar 2011

    Re: Adding and Subtracting Matrices

    because matrix arithmetic involves a lot of arithmetic operations "all at once", it is not uncommon to make various sign errors or other simple arithmetic mistakes in the process of doing one's calculations. i should know, this happens to me all the time.

    so one must be extra vigilant in checking and re-checking your work.

    it seems clear that what happened, is you added 8, instead of subtracting it (in the upper-right hand corner), other than that, everything is fine. your logic was fine, there was an error in execution (a sign error).
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