Proof on homogeneous equations

[toxi]

I need some help here... I've got the following assignment to do

Prove that if M>N then any system of N homogeneous equations in M unknowns has many solutions.

I am a bit stuck with this one. I thought about creating a MxN Matrix and to display the determinant with 1's.

and then say about the remaining colums after the rows with leading 1's stop (r = M-N), that they can represented by any value so there are many solutions
is that correct?

 

[ice109]

i don't know what you're saying but yes if you write down a matrix with M columns and N rows you'll see that you have a linearly dependent set of vector spanning the column space hence many solutions.