Find an orthogonal vector

I have the following matrix: M = [3 18 0;-3 -2 5;-1 5 0;3 3 -9]

I need to find a vector that's orthogonal to all of the vectors in this matrix. I'm familiar with how to solve for a vector that's orthogonal to two vectors (solving for lambda and multiplying lambda by a vector), but not sure how to solve for multiple vectors. Any help is appreciated!

Answer 1

[John D'Errico]

Never call a variable O. Consider how difficult it will be to find the bug one day, when you see or write a zero, instead of O. And consider that in some fonts, the difference between them is very slight.

As to the question, use null.

help null

[Samuel Hoppen]

Thanks, John. How exactly would you suggest using null? I tried null(M) (renamed the matrix), along with a couple other options, and that didn't give me the correct vector.

[James Tursa]

Why do you think null( ) did not give you the correct vector? What did it give you and what were you expecting differently?

[Samuel Hoppen]

Null(M) gave me a 3×0 empty double matrix. If I then calculate the dot product of null(M) and M, I get an error because the size of the vectors is different.