The given state equation is: H = Q Q -3


To find the eigen values of the given state equation, we need to solve the characteristic equation. The characteristic equation is given by:

|H - λI| = 0

where λ is the eigen value and I is the identity matrix.

Substituting the given state equation, we get:

|Q Q -3 - λI| = 0

Expanding the determinant, we get:

( Q - λ)( Q - 3 - λ) - Q( Q -3) = 0

Simplifying the above equation, we get:

λ^2 - 3λ - 2 = 0

Solving the quadratic equation, we get the eigen values as:

λ1 = -2
λ2 = -1

Therefore, the correct option is (a) -2,-4.


Eigen values are an important concept in linear algebra and are used in various applications such as image processing, data analysis, and machine learning. In this question, we are given a state equation and we need to find the eigen values. To do this, we first need to solve the characteristic equation, which is obtained by substituting the state equation in the determinant equation. Solving the characteristic equation gives us the eigen values. In this case, the characteristic equation is a quadratic equation, which can be solved using the quadratic formula. The eigen values obtained from the equation are -2 and -1, which are the correct answers for this question.