Question

Find the sum and the product of the Eigen values of the matrix = [ 2 −3 4 −2 ].

Answer 1

Step-by-step explanation:

Find the sum and the product of the Eigen values of the matrix = [ 2 −3 4 −2 ].

Answer 2

Given:

$\binom{2 \: \: \: \: \: \: \: - 3}{4 \: \: \: \: \: \: \: - 2}$

To Find:

The sum and the product of the Eigen values

Solution:

The sum of the Eigen values = Sum of the diagonal

= 2 + (-2) = 0

The product of the Eigen values = The modulus of the matrix

= 2(-2) - (4(-3))

= -4 - (-12) = -4 + 12 = 8

The sum and the product of the Eigen values of the given matrix are 0 and 8 respectively.