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Find a linearly independent set of vectors that spans the same subspace of R^4 as that...

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mrbest55 | Student | (Level 1) Salutatorian

Posted March 19, 2013 at 4:15 PM via web

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Find a linearly independent set of vectors that spans the same subspace of R^4 as that spanned by the vectors

 

Vector u = [[1],[2],[2],[-2]]

Vector v = [[-1],[3],[0],[3]]

Vector w = [[-7],[26],[2],[22]]

Vector x = [[-9],[-13],[-16],[19]]

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted March 20, 2013 at 10:08 AM (Answer #1)

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Find the a basis for the set of vectors.So  form a matrix, with each row being formed by a vector.

`[[1,2,2,-2],[-1,3,0,3],[-7,26,2,22],[-9,-13,-16,19]]`

Reduce it to row echelon form ( May be by Gaussian elimination) as.

`[[1,0,6/5,-12/5],[0,1,2/5,1/5],[0,0,0,0],[0,0,0,0]]`

 

This means that only two of the vectors in  set are linearly independent i.e. u and v vectors alone will span the same subspace of `RR^4`  as all four vectors.

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