- #1

- 83

- 0

## Homework Statement

Let A be an nxn matrix with real number entries, in which all entries are 1. Find the characteristic polynomial of A.

## Homework Equations

characteristic polynomial: f(t)=det(A-tI), I is identity matrix

## The Attempt at a Solution

I've tried to do this by various methods of induction, only to encounter massive blocks along the way. I can't really do anything with this past plug in numbers and hope something works. I know the equation should be (-1)

^{n}t

^{n-1}(t-n), but I don't know how to prove it. This is from a section of my book on invariant subspaces, is there anything I could do with those?