The characteristic equation of $A = \left( \begin{array} { c c }
2 & - 1 \
- 1 & 2
\end{array} \right)$ is
A) $\lambda ^ { 2 } - 1 = 0$
B) $\lambda ^ { 2 } + 4 \lambda + 5 = 0$
C) $\lambda ^ { 2 } - 4 \lambda + 5 = 0$
D) $\lambda ^ { 2 } + 4 \lambda + 3 = 0$
E) $\lambda ^ { 2 } - 4 \lambda + 3 = 0$

Question

The characteristic equation of $A = \left( \begin{array} { c c } 
2 & - 1 \
- 1 & 2
\end{array} \right)$ is
A) $\lambda ^ { 2 } - 1 = 0$
B) $\lambda ^ { 2 } + 4 \lambda + 5 = 0$
C) $\lambda ^ { 2 } - 4 \lambda + 5 = 0$
D) $\lambda ^ { 2 } + 4 \lambda + 3 = 0$
E) $\lambda ^ { 2 } - 4 \lambda + 3 = 0$

Quizplus · Accepted Answer

The characteristic equation is found by calculating the determinant of $A - \lambda I$, which results in $\lambda^2 - 4\lambda + 3 = 0$.

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

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