Hi
I'm told that three planes have the following equations:
3x+y−z=1x−y+kz=72x+ky−z=−1 Find the possible values of the constant k for which the equations do not have a unique solution.
I don't really understand what they're asking for.
Here's the worked solution for it (Q 8) but I'm afraid this doesn't help me much.
I understand that they've made the three equations in a singular matrix but why does this tell you the values for when "the equations do not have a unique solution"?
In summary, I don't understand the implications on the three equations if the value of k is
1 or
−32 (i.e. the values where the matrix of the three equations is singular).
I don't think this is strictly on my syllabus (I can't find it in any of my textbooks) but it'd be nice to understand it anyway.
Thank you