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Determine the largest eigen value and the corresponding eigen vector of the matrix A = 6 2 2 -2 3 -1 2 -1 3 by?

Determine the largest eigen value and the corresponding eigen vector of the
matrix A =
6 2 2
-2 3 -1
2 -1 3
by power method taking the initial vector as [1 1 1]pwr t.

Plz answer, my friends.

The equation for eigen values is:
det(A – λI) = 0
A is the matrix
I is the identity matrix
and λ is the eigenvalue

to solve for the eigenvalues solve the cubic equ.
λ^3 – tr(A)λ^2 + 0.5(tr(A)^2 – tr(A^2))λ – det(A) = 0

tr(A) is trace of A
det(A) is determinant of A

λ^3 – 12λ^2 + 44λ – 48 = 0

λ = 2, 4, 6

largest λ = 6

(A – λI) = [[0,, 2. 2]
…………..[-2 -3 -1]
…………..[2,,-1 -3]]

(A – λI)L = 0,
where L is the eigen vector = [L1;L2;L3]

Choose one of the values.
L1 = 1

[[-3 -1]..[[L2]..= [[2]
.[-1 -3]…[L3]]….[-2]]

L2 = -1,
L3 = 1

L = [1;-1;1]
normalized L = [0.57735; -0.57735; 0.57735]

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