Eigenvalues and Eigenvectors of a 2×2 Matrix
Consider the 2×2 matrix \(A = \begin{pmatrix}2 & 3\\1 & 4\end{pmatrix}\). Answer the following: (a) Calculate the trace and determinant of \(A\). (b) Find the eigenvalues of \(A\) by solving the characteristic equation \(\lambda^2 – (\text{trace})\lambda + (\text{det}) = 0\). (c) For each eigenvalue, determine a corresponding eigenvector of \(A\).