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quackensack

Member

Registered: 2007-02-27

Posts: 47

linear algebra problem

If someone could explain how this is done, I would really appreciate it!

Show that the characteristic polynomial of a 2 x 2 matrix A is given by x^2 - (trace(A))x+|A|.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: linear algebra problem

Definitions would be a good place to start. Let

What’s the definition of trace(A)? It’s the sum of the diagonal elements.

What’s the definition of |A|? Why, that’s the ubiquitous determinant.

And what’s the definition of the characteristic polynomial of A? Well, it’s the determinant of xI−A, where I is the identity 2×2 matrix.

Now put all these definitions together and, hey presto! You should have the required formula.

Last edited by JaneFairfax (2007-04-03 07:03:44)