Suppose that A = http://www.cramster.com/Answer-Board...1075009245.gif is a 2 x 2 real matrix with determinant -1. For what values of a,b,c and d will A be diagonalizable? Explain.

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- May 17th 2008, 04:34 AMmatty888Diagonalizable matrix!!(Not hard!)
Suppose that A = http://www.cramster.com/Answer-Board...1075009245.gif is a 2 x 2 real matrix with determinant -1. For what values of a,b,c and d will A be diagonalizable? Explain.

- May 17th 2008, 04:52 AMmr fantastic
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 ........