Find the characteristic polynomial of the matrix using eithe

Find the characteristic polynomial of the matrix, using either a cofactor expansion or the special formula for 3×3

determinants. [Note: Finding the characteristic polynomial of a 3×3 matrix is not easy to do with just row operations, because the variable is involved.]

Solution

Using cofcator expansion :

Characetreistic equation :

|A - xI | = ( 1-x)[ (4-x)(-x) +21 ] +0 [ ] +1 [-28]

= (1-x)[ x^2 -4x +21] - 28

= - x^3 +5x^2 - 25x -7