Question

If in a 3x3 matrix product of two eigen values
is 6 with determinant 6 then third eigen value is
"a 1
b. 2
d. 4
c. 3​

Answer 1

The third eigen value is 2 in the given matrix.

Given:
Eigen value = 6 and 6
To find: Third Eigen value

Solution:

Eigenvalues are the distinguished set of scalar principles that is guide the set of undeviating equatings most probably in the model equatings. The eigenvectors are again termed as characteristic ancestries. It is a non-nothing heading that can be exchanged merely by allure scalar factor afterwards the request of undeviating transformations.

By theorem we get,
Product of Eigen values = Determinant of matrix

Determinant of matrix = 6 × (9 – 1) – (- 2) (- 6 + 2) + 2 (2 - 6)

Determinant of matrix = 48 – 8 – 8

Then Determinant of matrix = 32

Let assume the third Eigen value be x

Product of Eigen value = Determinant of [A]

16 × x = 32
x = 2

So the third eigen value is 2.

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