## Eigenvalues

rinku.rohra85
Posts: 4
Joined: Wed Nov 27, 2013 3:31 pm

### Eigenvalues

Pls help me to solve the following equation :

What is the sum of the Eigen values of the matrix ?
7 -3
5 2

a) 8
b) 5
c) 9
d) 7
For any matrix A, Characteristics equation is given by, (A - λI) = 0
So, characteristics equation: λ2 - 9λ + 29 = 0
Sum of the Eigen values = 9

Finance Junkie
Posts: 258
Joined: Thu Sep 20, 2012 3:42 pm

### Eigenvalues

Matrix is :
7 -3
5 2
Characteristic Eqn is Obtained by subtracting a variable, say 'a' from diagonal elements. Here, a is the eigenvalue. Therefore, matrix now is:
7-a -3
5 2-a
Now, find determinant of matrix to get characteristic eqn, i.e
(7-a)(2-a) - (-3)(5)
= (a^2 -9a +14) +15
= a^2-9a+29

From properties of quadratic eqns, we have in a^2x + bx +c, sum of solutions of x = -b/a.

Therefore, sum of eigenvalues is 9/1=9

Finance Junkie
Posts: 258
Joined: Thu Sep 20, 2012 3:42 pm

### Eigenvalues

A linear operator is equivalent to finding the eigenvalues and eigenvectors of the associated square matrix .The are only used for square matrix . All matrices are assumed to be square.