Question: Let A denote the 2 x 2 matrix (a) Show that the characteristic equation of A (Eq. (3), Section 6.1) is given by (b) Suppose

Let A denote the 2 x 2 matrix

a b d C

(a) Show that the characteristic equation of A (Eq. (3), Section 6.1) is given by

(b) Suppose that the eigenvalues of A are pure imaginary. Show that the trace T (A) = a +d of A must be zero and that the determinant D(A) = ad - bc must be positive. Conclude that c ≠ 0.

a b d C

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