# Eigenvalues of 2x2 matrix

1. Nov 15, 2015

### whatisreality

1. The problem statement, all variables and given/known data
Find the eigenvalues of the matrix
$\left( \begin{array}{cc} 3 & -1.5\\ -1.5 & -1\\ \end{array} \right)$
It's probably a really stupid mistake, but the answer I get doesn't match the answer from wolfram alpha's eigenvalue calculator... always a bad sign.
2. Relevant equations

3. The attempt at a solution
The characteristic equation is:
(3-λ)(-1-λ) -$\frac{9}{4}$ = 0
→ λ2-2λ - $\frac{21}{4}$ = 0

λ = $\frac{2 \pm \sqrt{4 - (4\times -\frac{21}{4})}}{2}$
= $1 \pm \sqrt{25}$
= 6 or -4.

But apparently, I should be getting -1.5 and 3.5 . I have checked it so many times to see where I've gone wrong! What's the mistake??

2. Nov 15, 2015

### vela

Staff Emeritus
The 2 in the denominator divides into the entire numerator. You appeared to cancel it with the 2 from the -b part of the numerator, but ignored the rest of the numerator.

3. Nov 15, 2015

### Staff: Mentor

you lost 1/2 calculating λ. It's √25 / 2 and not √25

$\frac{a + b}{c} = \frac{a}{c} + \frac{b}{c}$

4. Nov 15, 2015

### whatisreality

You wouldn't believe how long I stared a that question. And didn't spot it. Thanks, I was getting so frustrated!

5. Nov 15, 2015

### Staff: Mentor

that happens sometimes and the honest of us aren't afraid to admit that it happens to them as well from time to time