The Characteristic Equation Of $A = \left( \begin{array} { c c c } 1 & - 12 & - 14 \\1 & 2 & - 3 \\1 & 1 & - 2\end{array} \right)$

The characteristic equation of $A = \left( \begin{array} { c c c } 1 & - 12 & - 14 \\1 & 2 & - 3 \\1 & 1 & - 2\end{array} \right)$ is

A) $- \lambda ^ { 3 } + \lambda ^ { 2 } + 25 \lambda - 25 = 0$
B) $- \lambda ^ { 3 } + \lambda ^ { 2 } - 25 \lambda + 25 = 0$
C) $- \lambda ^ { 3 } - \lambda ^ { 2 } + 25 \lambda - 25 = 0$
D) $- \lambda ^ { 3 } - \lambda ^ { 2 } - 25 \lambda + 25 = 0$
E) none of the above

Correct Answer:

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