hey folks,

I need help in one of my math question, hope somebody can help me, any hints, ideas, anything helps!!!

Suppose that A is a 2*2 matrix with real entries which is symmetric (A^t=A) Prove that A is similar over R to a diagonal matrix.

any help is welcome..

thanks
jyotsna,

maile 10 class ma gareko thiyo slc ko lagi. matrix sabai birsi satyo pasa sorry

is that Algebra related ? or Statistic ?

Since, undergrads are supposed to to their assignment themselves :-) , I will leave you with a hint here:

Every symmetric real square matrix can be diagonalized i.e.
If A is a n X n symmetric matrix then for an invertible matrix B, we have
A = B^(-1) D B , where D is a diagonal matrix.
Thus A is similar to D over R.

You have to prove this for n = 2.

Now , the hint:
Find the Eigen vectors and Eigen values of A. Create a matrix containing those Eigen vectors as its columns (Call it B). Then ,u will have
B A B^(-1) = D
where D is a diagonal matrix whose diagonal elements are the Eigen values of A.