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Math Help - Dimension of the subspace?

  1. #1
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    Dimension of the subspace?

    I have spent nearly the last hour trying to do this and im really stuck, the question is:
    Determine the dimension of the subspace spanned by the set
    { [1,−1,0], [6,−2,3], [6,−1,4] }.
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi

    You should check the value of the determinant of the three vectors. Either it is 0 and at least one vector is a linear combination of the two others. In this case ,the dimension of the subspace may be 0, 1 or 2 but has it is neither 0 nor 1 (why ?) it'll necessarily be 2. Either the value is not 0 and the subspace has dimension 3.

    \left|\begin{array}{ccc}<br />
1&6&6\\<br />
-1&-2&-1\\<br />
0&3&4<br />
\end{array}\right|=\ldots

    Good Luck
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  3. #3
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    The dimension of a basis for a subspace, is just the number of vectors contained in the basis, so in your case this would be 3.
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  4. #4
    Lord of certain Rings
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    Quote Originally Posted by skamoni View Post
    The dimension of a basis for a subspace, is just the number of vectors contained in the basis, so in your case this would be 3.
    Be careful skamoni, where did the question ever say that the subset is a basis?
    What if the set is linearly dependent?
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  5. #5
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    Fair enough, row reduce it first then.
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  6. #6
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    It's cheating a little bit, but I've found this program extremely useful for these questions:
    Linear Algebra Toolkit

    It's an on-line Linear Algebra programme, one of which determines whether set of vectors S is linearly independent or linearly dependent.

    For your problem it found that
    ...the set S = {v1, v2, v3} is linearly independent.
    Consequently, the set S forms a basis for span S.



    which should help you determine the dimension of the subspace
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