Let A denote the 2 2 matrix A D a b c d : (a) Show that
Chapter , Problem 39(choose chapter or problem)
Let A denote the 2 2 matrix A D a b c d : (a) Show that the characteristic equation of A (Eq. (8), Section 5.2) is given by 2 .a C d /C .ad bc/ D 0: (b) Suppose that the eigenvalues of A are pure imaginary. Show that the trace T .A/ D a C d of A must be zero and that the determinant D.A/ D ad bc must be positive. Conclude that c 6D 0. 4
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