Science:Math Exam Resources/Courses/MATH152/April 2022/Question B3 (a)/Solution 1

From UBC Wiki

Here is the argument for the standard procedure that computes the eigenvalues of a matrix. The equation

is equivalent to
This latter equation has a non-zero solution if and only if the matrix is not invertible, which is equivalent to . Therefore, we solve this last equation, since it is an equation of numbers (as opposed to an equation of vectors). We find the determinant to be

From the factorization above, we see that there are two eigenvalues of : -1 and 5, and 5 is called a repeated eigenvalue, since it shows up more than once in the factorization of .