Answer
P=−λ3+14λ+12
Work Step by Step
Given Information
We are given with an matrix A:
A=
0 3 1
3 0 2
1 2 0
We have to find the characteristic polynomial of above matrix.
Step-1: The characteristic Equation
Write the characteristic equation:|A−λI|=
0 3 1
3 0 2
1 2 0
−λ*
1 0 0
0 1 0
0 0 1
=
0 3 1
3 0 2
1 2 0
−
λ 0 0
0 λ 0
0 0 λ
=
−λ 3 1
3 −λ 2
1 2 −λ
Step-2: The characteristic polynomial
P=
−λ 3 1
3 −λ 2
1 2 −λ
=−λ(λ2−4)−3(−3λ−2)+1(6+λ)=−λ3+4λ+9λ+6+6+λ=−λ3+14λ+12
Hence, the characteristic polynomial is:
The characteristic polynomial is:
P=−λ3+14λ+12
