Find the eigenvalues and corresponding eigenvectors of 2 2 3

Find the eigenvalues and corresponding eigenvectors of [2 -2 -3 1].

Solution

|A - bI| = (2-b)(1-b) - (-3)(-2) = b^2 -3b +2 -6 = b^2-3b-4 = 0

or (b-1)(b+4) = 0

b=1 or b=-4

The 2 eigen values are b=1, b=-4

Inputting , b=1.

[1 -3

-2 0] [ v1 v2 ] = 0

So, v1 = 3v2

So, the first eigen vector is [1

-3]

The second eigen vector is by inputting b=-4,

[-2 -3

-2 -3] or

The second eigen vector is :

[ -2

-3]