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Math Help - Diagonalizable matrix!!(Not hard!)

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    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.
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    Quote Originally Posted by matty888 View Post
    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 ........
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