Find the characteristic polynomial of the matrix

Question

Find the characteristic polynomial of the matrix

[4 -2 0

 0 5 -4

 2 -5 0]

 

 

Answer 1

Set this determinant equal to zero, expand, simplify, and get a cubic polynomial in λ. That will be the characteristic polynomial:

|4 - λ -2 0|

|0 5 - λ -4|

|2 -5 -λ|