# Null(A) and cartesian form.

## Main Question or Discussion Point

Hi there,

just a pretty straight forward query I need cleared up.....

If a question asks for the null space of A in cartesian form how do I set it out?

This is what I've got:

X = ( -2; 1; 1)*x3 for all values of x3

Therefore, Null(A) corresponds geometrically to the line through the origin and (-2, 1, 1).

Now do I need to say that this is equivelant to -x = 2y = 2z for it to be in cartesian form or will the above suffice?

thanks for the help

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Office_Shredder
Staff Emeritus
Gold Member
I'm a bit confused. What is A, and how does that compare to X? Is X supposed to be the one dimensional vector space through the vector (-2,1,1)?

Yes, so AX = 0

where X = ( x1; x2; x3) and A = (1 0 2; 0 3 -3; 4 2 6)

which can be expressed as ( -2; 1; 1)*x3 after row reduction and back substitution.

I need to know whether I can leave it at that, or express it as the line: -x = 2y = 2z