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Math Help - Find a basis for W=span(v1,v2,v3) where v1 =...,v2=..., v3=... and state the dimensio

  1. #1
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    Find a basis for W=span(v1,v2,v3) where v1 =...,v2=..., v3=... and state the dimensio

    Find a basis for W=span(v1,v2,v3) where v1 =...,v2=..., v3=... and state the dimension of W.

    V1=(1,2,3) V2=(2,0,5) V3=(5,2,10)

    NOTE: After each comma is a new row. So these are all 1 column with 3 rows matrices.

    Can someone please give a clue how to start this question?
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  2. #2
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    Put v1, v2, v3 in a matrix and calculate the determinant. If the det is not equal to 0, then the 3 vectors form a basis. If the determinant is 0, do the reduced row echelon form to determine basis. Post your work if you need some help.
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  3. #3
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    Reply

    Thanks. So far yes I got the determinant but what does it mean when it says state the dimension of w? The determinant is 12.
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  4. #4
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    Since the determinant isn't 0, the vectors v1, v2, and v3 are the basis of W. The dimension is the number of vectors in the basis.
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  5. #5
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    Alright thanks.

    Alright thanks man!
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