Question

If A=1--21-20find the eigenvalues of the matrix A. Your answer should consist of two integers representing the two eigenvalues. Eigenvalue: Skipped Eigenvalue: Skipped

Answer 1

Eigenvalue: 0

Eigenvalue: 3

Explanation:

For any nxn matrix A, the eigenvalues of A are the y values that respect the following conditions

det(A - yI) = 0, where I is the order n identity matrix.

So A = [1 2; 1 2], I = [1 0; 0 1] yI = [y 0; 0 y]. In this notation, i have ; as a new line.

A - yI = [1-y 2; 1 2-y]

det(A - yI) = (1-y)*(2-y) - 2 = 0

= 2 - y - 2y + y² - 2 = 0

= y² - 3y = 0

= y(y-3) = 0

y = 0 or y - 3 = 0

y = 3