Show that the trace of a 3 × 3 matrix is equal to the sum of its eigenvalues using the following steps:  Find the characteristic polynomial  and show that the coefficient of 2 is the trace of  ...

Show that the trace of a 3 × 3 matrix is equal to the sum of its eigenvalues using the following steps:

 Find the characteristic polynomial
 and show that the coefficient of

²
is the trace of

 Explain why

<sub>1

2

3</sub>
 where the

_i
are the eigenvalues of

 Show that the coefficient of

²
is

<sub>1

2

3</sub>
 and argue that this completes the proof.