When you are finding the eigenvalues of a matrix, and find them by the determinant of (I*lambda - A) where A is the matrix, how would you proceed?

For example, one problem's determinant is (lambda - 8)(lambda + 1) - 18. What are the eigenvalues?

Question

When you are finding the eigenvalues of a matrix, and find them by the determinant of (I*lambda - A) where A is the matrix, how would you proceed?

For example, one problem's determinant is (lambda - 8)(lambda + 1) - 18.  What are the eigenvalues?

anonymous · Answer

(lambda - 8)(lambda + 1) - 18
multiply

anonymous · Answer

$$\lambda^{2} -7\lambda - 18 = 0$$

anonymous · Answer

-26*

anonymous · Answer

So now I have $$\lambda^2 -7\lambda -26$$ = 0.

Now I find the eigenvalues by plugging the coefficients into the quadratic formula, right?

anonymous · Answer

general method for solving a quadratic equation for example Ax^2+Bx+C would be as follows
first we are going to find the discriminant which is D= B^2 - 4*A*C
then roots (in this ques eigen values) will be x = -B± sqrt.(D)/2*A