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linear-algebra vector-spaces vectors

Dimension of the subspace of a vector space spanned by the following vectors.

发布于 2016-02-07 21:03:34

I know that in order to find a subsequence that is a basis of a subspace is to check whether the given vectors are linearly independent and whether they span the subspace.

However how can I find the dimensions of the subspaces of a vector space K^n ?

enter image description here

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NeoXx
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Bernard 2016-02-08 05:14:23

Hint:

Write the coordinates of the vectors as row vectors of a matrix, and perform row reduction of this matrix. The rank of the matrix will be the dimension of the subspace, and the non-zero lines in the final matrix will correspond to the vectors that span the subspace.

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