Home > Matrix Algebra calculators > Characteristic polynomial calculator

Solve any problem
(step by step solutions)
Input table (Matrix, Statistics)
Mode :
SolutionHelp
Solution
Find characteristic polynomial [[8,-6,2],[-6,7,-4],[2,-4,3]]

Solution:
Your problem `->` characteristic polynomial [[8,-6,2],[-6,7,-4],[2,-4,3]]


`|A-lamdaI|`

 = 
 `(8-lamda)`  `-6`  `2` 
 `-6`  `(7-lamda)`  `-4` 
 `2`  `-4`  `(3-lamda)` 


`=(8-lamda)((7-lamda) × (3-lamda) - (-4) × (-4))-(-6)((-6) × (3-lamda) - (-4) × 2)+2((-6) × (-4) - (7-lamda) × 2)`

`=(8-lamda)((21-10lamda+lamda^2)-16)+6((-18+6lamda)-(-8))+2(24-(14-2lamda))`

`=(8-lamda)(5-10lamda+lamda^2)+6(-10+6lamda)+2(10+2lamda)`

`= (40-85lamda+18lamda^2-lamda^3)+(-60+36lamda)+(20+4lamda)`

`=(-lamda^3+18lamda^2-45lamda)`

`=-lamda(lamda-3)(lamda-15)`






Solution provided by AtoZmath.com
Any wrong solution, solution improvement, feedback then Submit Here
Want to know about AtoZmath.com and me
  
 

Share with your friends
 
Copyright © 2018. All rights reserved. Terms, Privacy