Answer
P= −1(λ^3)+4(λ^2)−9λ−6
Work Step by Step
Finding Characteristic equation:
Given:
matrix A=
1 0 -1
2 3 -1
0 6 0
Step 1:
A−λI
A−λI =
(1-λ) 0 -1
2 (3-λ) -1
0 6 (0-λ)
Step 2:
Now take determinant of the above matrix
det (A-λI) = det of :
(1-λ) 0 -1
2 (3-λ) -1
0 6 (0-λ)
|A-λI| =
(1-λ) 0 -1
2 (3-λ) -1
0 6 (0-λ)
=(1−λ)[−3λ+(λ^2)+6]−0−1[12−0]
=(1−λ)[(λ^2)−3λ+6]−12
=(λ^2)−3λ+6−(λ^3)+3(λ^2)−6λ−12
=−λ^3+4(λ^2)−9λ−6
Hence, the characteristic polynomial is:
The characteristic polynomial is:
P= −1(λ^3)+4(λ^2)−9λ−6
