- #1

phrygian

- 80

- 0

## Homework Statement

Prove a symmetric (2x2) matrix always has real eigenvalues. The problem shows the matrix as {(a,b),(b,d)}.

## Homework Equations

The problem says to use the quadratic formula.

## The Attempt at a Solution

From the determinant I get (a-l)(d-l) - b^2 = 0 which expands to l^2 - (a+d)l + (ad - b^2) = 0

Using the quadratic formula I get for under the square root: (a + d)^2 - 4(ad-b^2)

How can I show that this is always positive?

Thanks for the help