# Math Help - confused about finding another vector to form a basis

1. ## confused about finding another vector to form a basis

I got a basis of kernel of a 2*4 matrix :

$(-5,1,-3,0)^{T}, (10,0,7,1)^{T}$

now, i found a vector:
$(0,2,1,1)^{T}$
how can i find another vector together with this form a basis of kernel?

2. This is basis transformation issue.

v1=(-5,1,-3,0)^{T}, v2=(10,0,7,1)^{T}
w1=[v1 v2][2 1]^{T}
example:
w2=[v1 v2][1 1]^{T}, or [v1 v2][1 2]^{T}

If [w1 w2]=[v1 v2]A, matrix A must be invertible
w2 = [5 1 4 1] or [15 1 11 2]