Matrix Eigenvalues calculator

SolutionHelp

[8-62-67-42-43] $[[8,-6,2],[-6,7,-4],[2,-4,3]]$

[6-22-23-12-13] $[[6,-2,2],[-2,3,-1],[2,-1,3]]$

[324202423] $[[3,2,4],[2,0,2],[4,2,3]]$

[111-1-3-3244] $[[1,1,1],[-1,-3,-3],[2,4,4]]$

[23410] $[[2,3],[4,10]]$

[5142] $[[5,1],[4,2]]$

Example

1. [8-62-67-42-43] $[[8,-6,2],[-6,7,-4],[2,-4,3]]$
Find eigenvalues ...

|A-λI|=0 $|A-lamdaI|=0$

|(8-λ)-62-6(7-λ)-42-4(3-λ)|=0 $|[(8-lamda),-6,2],[-6,(7-lamda),-4],[2,-4,(3-lamda)]|=0$

(8-λ)((7-λ)×(3-λ)-(-4)×(-4))-(-6)((-6)×(3-λ)-(-4)×2)+2((-6)×(-4)-(7-λ)×2)=0 $(8-lamda)((7-lamda) × (3-lamda) - (-4) × (-4))-(-6)((-6) × (3-lamda) - (-4) × 2)+2((-6) × (-4) - (7-lamda) × 2)=0$

(8-λ)((21-10λ+λ2)-16)+6((-18+6λ)-(-8))+2(24-(14-2λ))=0 $(8-lamda)((21-10lamda+lamda^2)-16)+6((-18+6lamda)-(-8))+2(24-(14-2lamda))=0$

(8-λ)(5-10λ+λ2)+6(-10+6λ)+2(10+2λ)=0 $(8-lamda)(5-10lamda+lamda^2)+6(-10+6lamda)+2(10+2lamda)=0$

(40-85λ+18λ2-λ3)+(-60+36λ)+(20+4λ)=0 $(40-85lamda+18lamda^2-lamda^3)+(-60+36lamda)+(20+4lamda)=0$

(-λ3+18λ2-45λ)=0 $(-lamda^3+18lamda^2-45lamda)=0$

-λ(λ-3)(λ-15)=0 $-lamda(lamda-3)(lamda-15)=0$

$:.$ the eigenvalues of the matrix A are given by

$lamda=0,3,15$