Question

(6 -6 5
14 -13 10
7 -6 4)
eigen value

Answer 1

Step-by-step explanation:

Here is your answer ......

Answer 2

To find the eigenvalues, we need to calculate the determinant of the matrix A-λI.

|A - λI| = |(6 -6 5) - λ(1 0 0)|

|(14 -13 10) - λ(0 1 0)|

|(7 -6 4) - λ(0 0 1)|

Expanding the determinant of the matrix gives:

|A - λI| = (6-λ) * ((-13-λ)(4-(-6-λ)) - (-6)(10-(-6-λ))) - (-6)((-13-λ)(7-(-6-λ)) - (-6)(14-(-6-λ))) + 5((-13-λ)(7-(-6-λ)) - (-6)(14-(-6-λ)))

This simplifies to:

|A - λI| = (6-λ)(-13-λ+10-λ+6+λ) - (-6)(-13-λ+7-λ+6+λ) + 5(-13-λ+7-λ+6+λ)

= (6-λ)(-7-λ) - (-6)(-7-λ) + 5(-7-λ)

= (6-λ)(-7-λ) + 6(7+λ) + 35(7+λ)

= -7λ^2 - 13λ + 42 + 42λ + 210 + 245λ

= -λ^2 - 20λ + 697

So the eigenvalues of the matrix are the roots of the characteristic polynomial, which is -λ^2 - 20λ + 697 = 0.

Therefore, the eigenvalues of the matrix are:

λ1 = (20 + √(20^2 - 4697)) / 2 = 10 + √(196)

λ2 = (20 - √(20^2 - 4697)) / 2 = 10 - √(196)

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