Thread: Diagonalizable matrix!!(Not hard!)

Suppose that A = is a 2 x 2 real matrix with determinant -1. For what values of a,b,c and d will A be diagonalizable? Explain.

Originally Posted by matty888

Suppose that A = is a 2 x 2 real matrix with determinant -1. For what values of a,b,c and d will A be diagonalizable? Explain.

Using the fact that det(A) = -1 you should be able to establish that A has two distinct eigenvalues.

Now recall that an n x n matrix A is diagonalizable over the field F if it has n distinct eigenvalues in F, that is, if its characteristic polynomial has n distinct roots in F.

Therefore ........