The Characteristic Equation for the Matrix $A = \left( \begin{array} { c c c } 3 & 0 & 0 \\0 & 1 & - 1 \\0 & 1 & 3\end{array} \right)$

Multiple Choice

The characteristic equation for the matrix $A = \left( \begin{array} { c c c } 3 & 0 & 0 \\0 & 1 & - 1 \\0 & 1 & 3\end{array} \right)$ is

A) $- \lambda ^ { 3 } - 7 \lambda ^ { 2 } - 16 \lambda + 12 = 0$
B) $- \lambda ^ { 3 } + 7 \lambda ^ { 2 } + 14 \lambda + 6 = 0$
C) $- \lambda ^ { 3 } + 7 \lambda ^ { 2 } - 14 \lambda + 6 = 0$
D) $- \lambda ^ { 3 } + 7 \lambda ^ { 2 } + 16 \lambda + 12 = 0$
E) $- \lambda ^ { 3 } + 7 \lambda ^ { 2 } - 16 \lambda + 12 = 0$