Question

What are the eigenvalues of the matrix A = [2 3; 2 1]?

a) 4, -1
b) 3, 2
c) 1, 2
d) -4, 1

Answer 1

The eigenvalues of matrix A = [[2, 3], [2, 1]] are 4 and -1.

Step-by-step explanation:

The eigenvalues of a matrix can be found by solving the characteristic equation. For matrix A = [[2, 3], [2, 1]], the characteristic equation is found by subtracting the identity matrix multiplied by a scalar λ from matrix A and taking the determinant. So, A - λI = [[2-λ, 3], [2, 1-λ]]. The determinant of this matrix is (2-λ)(1-λ) - 3 * 2 = λ^2 - 3λ -4, which can be factored as (λ-4)(λ+1).

Therefore, the eigenvalues of matrix A are λ = 4 and λ = -1. So, the correct answer is option a) 4, -1.