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Homework Help: Matrix Space, dependence/indepence (HELP!)

  1. Oct 22, 2009 #1
    1. The problem statement, all variables and given/known data

    Is this set of 2x2 matrices linearly independent or dependent in M2,2 (the space of 2x2 matrices)

    Matrix 1 (2x2)
    [ 1 4 ]
    [ -1 3 ]

    Matrix 2 (2x2)
    [ -1 5]
    [ 6 2]

    Matrix 3 (2x2)
    [ 1 13]
    [ 4 7]

    3. The attempt at a solution

    I know that I need to set r1M1 + r2M2 + r2M3 = 0

    and then make some equations = 0
    then put those in a matrix
    make that matrix part of a linear system
    do row reduction
    if trivial solutions exist then it's independent
    if trivial solutions don't exist

    I HAVE NO CLUE HOW TO DO THE FIRST STEP THOUGH, never seen an example with matrices. HELP!
  2. jcsd
  3. Oct 22, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You know that a constant times a matrix multiplies each element of the matrix, right?

    And in your equation r1M1 + r2M2 + r3M3 = 0 the zero in the right side is the zero matrix, right? So write out the matrix equation you get and equate the elements.
  4. Oct 22, 2009 #3
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