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Math Help - Determining Linear Independence

  1. #1
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    Determining Linear Independence

    Three 2X2 matrices:

    [2 3]
    [1 1]

    [-1 2]
    [ 0 0]

    [1 0]
    [0 1]

    How do I show if this set of elements in linearly dependent or not? Thanks,

    Jim
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  2. #2
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    lin dependance

    For memory, two vectors in R^2 are linear dependant if and only if they one is a multiple of each other,

    so something such as

    [2 2] <---- v1
    [1 1] <---- v2

    (vector 1 is top row, vector 2 is bottom row)
    would be linear dependant because v2 = 2(v1)

    therefore,

    [2 3] is linear independant as v2 isnt a multiple of v1
    [1 1]

    [-1 2] is linear dependant since v2 is the zero vector 0(v1) = v2
    [ 0 0]

    [1 0] is the identity matrix 2 therefore it is linear independant
    [0 1]


    Not sure if I'm 100% correct but if its urgent then I hope it helps
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  3. #3
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    Hey Martinr,

    Thanks! This is a big help.

    Jim
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  4. #4
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    Quote Originally Posted by Jim Newt View Post
    Three 2X2 matrices:

    [2 3]
    [1 1]

    [-1 2]
    [ 0 0]

    [1 0]
    [0 1]

    How do I show if this set of elements in linearly dependent or not? Thanks,

    Jim
    If you are considering the matrices themselves as vectors, clearly they are linearly independent, because 2 row 1 column co-ordinate is 0 in two matrices and non-zero in the remaining. No linear combination of 0s can give a 1.
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  5. #5
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    But what if you were to consider the three matrices as a set instead of looking at each matrix as its own set? How would you go about determining whether the set of three matrices were independent or dependent?
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