Simple Linear algebra question

[Johnny5]

I want to solve a problem, to help me recall some more linear algebra.

 

I want to solve a matrix system, and I want the answer to be a straight line in three dimensional space.

 

So intuitively, i know this:

 

If two planes are parallel they have absolutely no points in common, but

 

If they are not parallel then they do have points in common, and

 

the set of all points they have have in common lie on one and only one infinite straight line.

 

Now, i know that the form of an equation for a plane in three dimensional space is:

 

Ax+By+Cz=0

 

So choose two planes from the set of planes, but make sure they are not parallel.

 

At this point, i want to solve a system of simultaneous linear equations, and write my answer in the form of an arbitrary straight line in 3D space.

 

This is the part I cannot remember how to do.

 

Thank you

[Asimov Pupil]

do you mean solving the system using row reduction, or taking your reduced form and solving for the vector(s) that for the basis of that vector space?

[ydoaPs]

do you mean solving the system using row reduction, or taking your reduced form and solving for the vector(s) that for the basis of that vector space?

he can't answer. he was banned long ago.