5) Let A be an n × n matrix. Show that any collection of eigenvectors of A corresponding to different eigenvalues is linearly independent. (Hint: Need show general case, can be proved directly or by...

I need prove linear independence of eigrnvectors.

I posted this before and just showed me with 2 vectors.

I need general case which apparantly can be proved directly.

Thanks

Extracted text: 5) Let A be an n × n matrix. Show that any collection of eigenvectors of A corresponding to different eigenvalues is linearly independent. (Hint: Need show general case, can be proved directly or by induction)