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Math Help - Linear algebra question

  1. #1
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    Linear algebra question

    If anyone could explain how the following is done, it would be greatly appreciated.

    Give an example of the following. If no example exists, explain why.

    - A set of vectors in M sub 3,4 which are linearly independent but do not span M sub 3, 4
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by faure72 View Post
    If anyone could explain how the following is done, it would be greatly appreciated.

    Give an example of the following. If no example exists, explain why.

    - A set of vectors in M sub 3,4 which are linearly independent but do not span M sub 3, 4
    Assuming that M_{3,4} denotes the set of all 3x4 matrices (over R?)

    [1,0,0,0]
    [0,0,0,0]
    [0,0,0.0]

    and

    [0,1,0,0]
    [1,0,0,0]
    [0,0,0,0]

    are linearly independent and do not span M_{3,4} and so are the elements
    of a set with the desired property.

    RonL
    Last edited by CaptainBlack; May 6th 2007 at 01:44 AM. Reason: to avoid anyone knowing that he made a mistake!
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by CaptainBlack View Post
    Assuming that M_{3,4} denotes the set of all 3x4 matrices (over R?)

    [1,0,0,0]
    [0,0,0,0]

    and

    [0,1,0,0]
    [1,0,0,0]

    are linearly independent and do not span M_{3,4} and so are the elements
    of a set with the desired property.

    RonL
    would not those matrices need a third row? since they have to be elements of M_{3,4}?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Jhevon View Post
    would not those matrices need a third row? since they have to be elements of M_{3,4}?
    Opps.. yes of course (goes back and modifies post so no one will ever
    know CB made a mistake )

    RonL
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