finding characteristic polynomial, problem with the question?

Hi.

I was asked to find the characteristic polynomial of A.

A has the following attributes:

I argue that there is a contradiction here!

if , it means that: .

if then it means that the diagonal matrix D (who has the eignvalues on it's main diagonal), has some in its entry, and the rest are zeroes. meaning, D looks like this:

now, the problem is, that , and since the trace is the sum of the eignvalues, we'll get that , and that means that ! (and not 1 as stated in the question)

Re: finding characteristic polynomial, problem with the question?

Hi,

I think you'd best rethink your analysis. Does the following matrix satisfy the conditions?

What is the characteristic polynomial of A?

Re: finding characteristic polynomial, problem with the question?

OK, now I see what was wrong with my analysis.

I thought that elementary row operations doesn't change the transformation.

dunno why...