🔷14 - Eigenvalues and Eigenvectors of a 2x2 Matrix

🔷14 - Eigenvalues and Eigenvectors of a 2x2 Matrix Given that A is a square matrix (nxn), Ax = kx -------(1), where A = an nxn matrix (square matrix), x = eigenvector of A corresponding to k, k = eigenvalue of A corresponding to x It is usually asked to find the eigenvalue as well as the eigenvector that satisfy the above equation. Notice that we are only interested in the solution with x not equal to zero. from (1), Ax = kx Ax = kIx ------(2) , (A-kI)x = 0 ----(3) the system will give a non-zero solution if and only if det (A-kI)x = 0 , det (A-kI) gives rise to a polynomial called the characteristic polynomial and the equation formed when det (A-kI) = 0 is called the characteristic equation. The solutions to the equation are the eigenvalues.... Visit channel Playlist for more videos on Engineering mathematics, applied electricity and Basic Mechanics. Kindly support and Subscribe Thank you 00:00 - Eigenvalues and eigenvectors 05:44 - Example