Question

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.

Answer 1

@amistre64

Answer 2

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

Answer 3

sum of the main diag ...

Answer 4

but then A^2 has me befuddled

Answer 5

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