#appliedcourse

Question

not getting the answer by 3*3 eigen value formula – (x^3-trace(a)*x^2+sum of minors of a(x)+|a|)

eigen values are given as -2,3,6

Answer 1

The eigen values come out to be -2,3,6.
Questions ask the sum of maximum and minimum eigenvalues which is $6 +(-2)= 4$.
Hence 4 is correct.

Edit: my bad i misunderstood your doubt.

I Solved it using the traditional method. 
I basically calculated the determining along column 2. 
See my calculations below.
 

at last $\lambda = -2,6,3$

Comments

By the below-updated formula, I am getting the correct eigenvalues.

x^3-b1*x^2+b2*x-b3=0

where,

b1=trace of matrix

b2=sum of minors of diagonal elements of the matrix

b3=mod of matrix (mod|A|)

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@Dknights i have updated my answer. regarding the equation you gave, i have no idea how you arrived at it. is this some new way to calculate eigen values ?