DATA 605 Discussion Week 3

Find the characteristic polynomial of the matrix A.
A =\(\begin{bmatrix}1 & 2 \\3 & 4\end{bmatrix}\)

To solve we will use the equation det(A−λI)=0

A−λI =\(\begin{bmatrix}1-λ & 2 \\3 & 4-λ\end{bmatrix}\)

Solve for λ: \[{det(A−λI)= (1-λ)(4-λ) - (2)(3) }\] \[{det(A−λI)=(λ^2-5λ+4)-6}\] \[{det(A−λI)=λ^2-5λ-2}\]

Answer The characteristic polynominal is \[{λ^2-5λ-2}\]