Math Help - Basis and eigenvectors

1. Basis and eigenvectors

Can R^3 have a basis of eigenvectors all of which have 0 in their first components, why or why not? Thank you in advance for your time.

2. Re: Basis and eigenvectors

Originally Posted by nivek0078
Can R^3 have a basis of eigenvectors all of which have 0 in their first components, why or why not? Thank you in advance for your time.
No, the rank of those three vectores is $<3.$