C:10 - Find the characteristic polynomial of the matrix A

A <- matrix(c(1,3,2,4), nrow=2, ncol=2) 

\[\mathbf{A} = \left[\begin{array} {rrr} 1 & 2 \\ 3 & 4 \\ \end{array}\right] \]

\[\mathbf{A} = \left[\begin{array} {rrr} 1-\lambda & 2 \\ 3 & 4-\lambda \\ \end{array}\right] \]
\[ (1-\lambda)(4-\lambda)-6 = 0 \]

\[ (4-4\lambda-\lambda+\lambda^2-6) =0 \]

\[ Characteristics Equation = \lambda^2-5\lambda-2=0 \]