Find the characteristic polynomial of the matrices begin{bmatrix}1 & 2&1 0 & 1&2-1&3&2 end{bmatrix}

Jason Farmer

Jason Farmer

Answered question

2021-02-27

Find the characteristic polynomial of the matrices
[121012132]

Answer & Explanation

Asma Vang

Asma Vang

Skilled2021-02-28Added 93 answers

Step 1
Given:
Let A=[121012132]
To Find: Characteristic polynomial of the given matrices
Step 2
Solution:
A=[121012132]
AλI=[1λ2101λ2132λ]
Characteristic polynomial of matrix A is given by |AλI|=0
[1λ2101λ2132λ]=0
(1λ)[(1λ)(2λ)6]2[0+2]+1[0+(1λ)]=0
(1λ)(2λ2λ+λ26)4+1λ=0
After simplifying we get
λ34λ2+7=0
Hence this is the required characteristic polynomial of given matrix.
Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-27Added 2605 answers

Answer is given below (on video)

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