Answer:
Eigenvalue: 0
Eigenvalue: 3
Step-by-step 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
