Math Is Fun Forum

mathsyperson wrote:

Using the fact that AX=0 has the trivial solution won't help you, as your teacher pointed out.
What you need to use is that it has just the trivial solution. That means that no other matrix X will fit the equation, and you should be able to use that to help you.

Also, keep in mind that it is an 'if and only if' proof, which means that you need to prove that if A has rank n then AX=0 has no non-trivial solutions, and that if AX=0 has no non-trivial solutions then A has rank n.

Okay, but where I'm stuck is that I'm not sure how to prove that if A has rank n, then AX=0 has no non-trivial solutions.

No?

I was suggesting that you research the name, not simply make an absurd assumption.