# Shortcut to find if a matrix (nxn) is singular or not?

1. Jan 28, 2010

### dlevanchuk

Is there a quick shortcut to find if a matrix (nxn) is singular or not?

For example, if the matrix is (2x2), and $$\Delta$$ (i.e. ad-bc) = 0, then matrx is singular and irrevertable..

Is there something similar for (nxn), like (3x3) and (100, 100), without doing the linear independence?

2. Jan 28, 2010

Re: shortcut?

There are different ways to see if a matrix is singular or not, but all of them requires some calculation, as far as I know.

3. Jan 28, 2010

### dlevanchuk

Re: shortcut?

then what would be the fastest way to check the singularity of matrix?

lets say my (3x3) matrix is A = [1 2 3; 1 3 2; 1 1 4]. Obviously, if we set Ax = 0, and do G/J elimination we find that this particular matrix is singular... but, man! It takes forever haha.

4. Jan 28, 2010

Re: shortcut?

Try to find its eigenvalues - if one of them is 0, then A is singular.

5. Jan 28, 2010

### Rasalhague

Re: shortcut?

Yes, it's called the determinant, but it's not practical to do by hand for big matrices. Luckily there are computers...

http://www.wolframalpha.com/input/?i=det{{1%2C+2%2C+3}%2C+{1%2C+3%2C+2}%2C+{1%2C+1%2C+4}}