\[ \left[ {\begin{array}{cc} 1 & 2 \\ 3 & 4 \\ \end{array} } \right] \]
Christian’s Response:
Equation to get characteristic polynomial:
\(det(A-\lambda\mathit{I}_n)\)
Solve for the following
\[ \left[ {\begin{array}{cc} 1 & 2 \\ 3 & 4 \\ \end{array} } \right] - \left[ {\begin{array}{cc} \lambda & 0 \\ 0 & \lambda \\ \end{array} } \right] \]
Subtract A and \(\lambda\)
\[ \left[ {\begin{array}{cc} 1-\lambda & 2 \\ 3 & 4-\lambda \\ \end{array} } \right] \]
Breakdown equation
\((1-\lambda)(4-\lambda)-6\)
Characteristic polynomial below
\(\lambda^2-5\lambda-2\)