Why must every homogeneous system of planes have at least 1 intersection point

[singleton]

Well, I'm doing homework (again).

I was introduced to homogeneous systems of planes and then asked why there must be at least 1 intersection point.

The book gives very little (one sentence) on homogeneous systems so I tried to search around online.

My guess is that since all of the planes pass through the origin (right?), then they have this in common and thus have at least one point of intersection?

 

[rachmaninoff]

My guess is that since all of the planes pass through the origin (right?), then they have this in common and thus have at least one point of intersection?
singleton is offline Report Bad Post Reply With Quote

Yup. The point '0' is a solution to any homogenous equation; so it's a point of intersection of the solution sets of any set of homogenous equations, planes or otherwise.