## rock_mit182 one year ago a) Show that the eigenvalues of the 2 X 2 matrix A = [a,b];[c,d] are the solutions of the quadratic equation A^2 - tr(A)lambda + det A = 0, where tr(A) is the trace of A.

1. rock_mit182

@amistre64

2. amistre64

i thought AA was just another matrix ... the trace and det are scalars if memory serves also, refresh my memory on the definition of the trace

3. amistre64

sum of the main diag ...

4. amistre64

but then A^2 has me befuddled

5. Michele_Laino

hint: we can write the subsequent quadratic equation: $\det \left( {\begin{array}{*{20}{c}} {a - \lambda }&b \\ c&{d - \lambda } \end{array}} \right) = {\lambda ^2} - \left( {a + d} \right)\lambda + ad - bc$