Finding a Matrix whose kernel is spanned by 2 vectors

[DanceLink]

Homework Statement

Find a matrix whose kernel is spanned by the two vectors u=(1,3,2) and v=(-2,0,4).

Homework Equations

The Attempt at a Solution

Tried setting vectors as a matrix and rref'ing it, but didn't know where I was getting at, also tried using an augmented identity matrix with both vectors then realized I didn't know what I was doing.

 

[Dick]

How about finding a vector w that's orthogonal to both u and v and making a matrix where all of the rows are w?

 

[DanceLink]

k I think I got it...
Given:
u=[1,3,2]
v=[-2,0,4]

I put in the vector M(1)=[1,1,1]
M:=<u|v|M(1)>
and I get...
[1,-2,1
3,0,1
2,4,1]

I apply rref, and I get an identity matrix. Meaning that the above matrix is my answer, right?

 

[Dick]

That doesn't work. M*u is (-3,5,14) isn't it? If u is in the kernel M*u is supposed to (0,0,0). I don't think you heard me. Find a vector w so that u.w=0 and v.w=0. Wouldn't it work if you make a matrix with all of the rows w?