# Thread: Find a set of vectors whose span is the kernel of the following matrix.

1. ## Find a set of vectors whose span is the kernel of the following matrix.

Find a set of vectors whose span is the kernel of the following matrix:

1 1 2 0
2 1 0 -1
0 1 4 1

When I calculate the kernel I get:

2s+t
-4s-t
s
t

To find the set of vectors that span this kernel do I factor out the s and t?

s * [2, -4, 1, 0]T + t * [1, -1, 0, 1]T

Am I close on this one?

2. ## Re: Find a set of vectors whose span is the kernel of the following matrix.

correct

The two vectors $\displaystyle \{\{1,-1,0,1\},\{2,-4,1,0\}\}$ form a basis for the kernel of the matrix

3. ## Re: Find a set of vectors whose span is the kernel of the following matrix.

So I am assuming that I would leave out the constant multipliers s and t?

4. ## Re: Find a set of vectors whose span is the kernel of the following matrix.

Saying that "{{1, -1, 0, 1}, {2, -4, 1 , 0}} is a basis for the kernel" means that any vector in the kernel can be written in the form s{1, -1, 0, 1}+ t{2, -4, 1, 0} for numbers s and t. Those are just two different ways of saying the same thing.