I have been trying to solve the following problem:
The coefficient of $\lambda^{3}$ in the characteristic polynomial $f(\lambda)$ of \begin{pmatrix} 2 &3 &0 &1 \\ 4&-1 &0 &0 \\ 0&3 &-4 &8 \\ 2&1 &-4 &2 \end{pmatrix} is
(a) $2$
(b) $3$
(c) $0$
(d) $1$.
My question is: Is there any other way to find the coefficient of $\lambda^{3}$,apart from finding the characteristic polynomial of the given matrix? I have solved it by finding the characteristic polynomial which is lengthy. Any other alternative suggestions to tackle the problem in a better way will be appreciated. Thanks in advance for your time.