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Matrice Multiplication, can someone check my work?

  1. Mar 14, 2012 #1
    1. The problem statement, all variables and given/known data
    Its a 3x2 multiplying a 2x2. (3 down 2 across, 3x2) I was gone for the day that my teacher explained it to us, and I am not sure how to do it. I tried, but I want to be sure.



    2. Relevant equations
    5 2
    0 -4 _X_ 3 7
    1 6 ___ -2 0


    3. The attempt at a solution
    The answer I got was
    18 42
    -8 0

    Can one of you intellectuals tell me if I got the right answer?

    EDIT: I realized I didn't actually tell you what I did. I took the first column of numbers in the first matrix (5, 0, 1), and added together the products of it and the first number in the first column (3). I took the 3 numbers from the second column (2, -4, 6) and added the products of them and the first number in the second column (7). I repeated that with the -2 and the 0.
     
    Last edited: Mar 14, 2012
  2. jcsd
  3. Mar 14, 2012 #2
    You're not multiplying the matrices correctly. Here is what you should do:

    [itex]
    \left(
    \begin{array}{cc}
    a & b\\
    c & d\\
    e & f
    \end{array}
    \right) \cdot
    \left(
    \begin{array}{cc}
    g & h\\
    i & j\\
    \end{array}
    \right) =
    \left(
    \begin{array}{cc}
    ag + bi & ah + bj\\
    cg + di & ch + dj\\
    eg + fi & eh + fj
    \end{array}
    \right)
    [/itex]

    You have a 3x2 (rows x columns) multiplied by a 2x2 matrix. When multiplying, the "inside" two numbers cancel out and the resulting matrix is the dimensions of the outside numbers. So, for example, a 4x3 matrix multiplied by a 3x1 matrix would yield a 4x1 matrix. The inside numbers MUST match, otherwise it's not valid to multiply them.

    Try to redo your problem and see what you come up with!
     
  4. Mar 14, 2012 #3
    This time I got
    11 35
    8 0
    -9 7

    Is that right?
     
  5. Mar 14, 2012 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    The singular of the (plural) word matrices, is the word matrix.
     
  6. Mar 14, 2012 #5
    That answer looks good! And what Sammy posted is also correct, I didn't catch that any of the times I glanced at the subject.
     
  7. Mar 14, 2012 #6

    Mark44

    Staff: Mentor

    And matrice is not a word. Those Romans with their Latin language and weird plurals are to blame. Some other Latin-derived words with the same pluralization rules are appendix, aviatrix (female aviator), and circatrix (scar tissue).
     
  8. Mar 14, 2012 #7
    Well, linguistic debates aside, I checked in the back of the book in the selected answers, and it seems I got it right. Thanks for the help, but I have another problem so I posted another thread.
     
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