# Finding a Matrix whose kernel is spanned by 2 vectors

## Homework Statement

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

## 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.

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Dick
Homework Helper
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?

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