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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.
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.

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amistre64
 one year ago
Best ResponseYou've already chosen the best response.0i 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

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0sum of the main diag ...

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0but then A^2 has me befuddled

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.1hint: we can write the subsequent quadratic equation: \[\det \left( {\begin{array}{*{20}{c}} {a  \lambda }&b \\ c&{d  \lambda } \end{array}} \right) = {\lambda ^2}  \left( {a + d} \right)\lambda + ad  bc\]
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