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Math Help - Matrices question

  1. #1
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    Matrices question

    \begin{bmatrix} 2a+b & -a+b \\ a-b & 3a-2b \end{bmatrix}-\begin{bmatrix} 2a-b & b \\ 4a+b & 2b \end{bmatrix}

    Working through the above problem, an instructional video tells me to solve row 1, column 1 of the matrices as follows;

    2a+b - (2a - b)

    The video then goes onto used the disributive property, assuming a negative "1" in front of the parentheses, thus "negative 1 multiplied by negative 2a"

    Is this correct? The reason I am asking is because I thought it would be negative 1 multipled by positive 2a, as there isn't a sign within the parentheses?

    The video I am watching solves the equation as follows;
    2a + b - (2a - b)
    = 2a + b - 2a + b
    = 2a - 2a + b + b
    = 2b

    I can follow the rest of the solution, I am just confused as to why the teacher assumes a negative sign in front of the 2a which is within the parentheses.
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: Matrices question

    Hi Layman!

    You are absolutely right.
    It should be "negative 1 multipled by positive 2a".
    This is also exactly what was done in the solution.
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  3. #3
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    Re: Matrices question

    Thanks ILikeserena - it seems the instructor made a verbal slip.
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