Basic Linear Algebra Proof
Consider the homogeneous system of linear equations
Prove that if , then is the only solution to the system.
First, I tried rewriting the system of equations to get and . This would have probably helped me in the proof, but I realized that I may not be able to divide by and because they may be .
Maybe I could use the contrapositive to prove this. Proving the statement "If , then is not the only solution to the system. I'd have to show that there are more solutions. I am not sure how to do this though. Although, this seems like the easiest way to prove it.
Can anyone give me some help? Thanks in advance.