Linear algebra question.

Question

Let W=Span(（1 1 1 3）（1 2 1 4）（2 3 3 8）and C = （v₁, v₂, v₃, v₄, v₅）where v₁(1 0 1 2), v₂=(0 1 1 2), v₃(2 -1 1 2), v₄=(1 1 2 4), v₅=(2 1 4 7). 

 

Find a subsequence of C which is basic of W. If there is no subsequence write NONE.

Answer 1

Only one of the vectors from C can be used to form the basis, as a 4 x 4 matrix is needed.

 

 Testing each one of them, one at a time, using an online calculator to convert the matrix

 

 to reduced row echelon form (rref) , NONE OF THEM WORK.

 

Here's the link to the online calculator for finding rref

 

http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi?c=rref