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

1. ## 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?

2. 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.

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.

4. 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.

5. ## Alright thanks.

Alright thanks man!