Question

The determinant |F-λI|=0 yields the characteristic polynomial of the matrix F.

(a) True

(b) False

I had been asked this question in examination.

My doubt is from State-Space System Analysis and Structures in portion Discrete Time Systems Implementation of Digital Signal Processing

Answer 1

Right answer is (a) True

Best explanation: We know that (F-λI)U=0

The above equation has a nonzero solution U if the matrix F-λI is singular, which is the case if the determinant of (F-λI) is zero. That is, |F-λI|=0.

This determinant yields the characteristic polynomial of the matrix F.