Linear Algebra Example Problems - Basis for an Eigenspace

http://adampanagos.org Course website: https://www.adampanagos.org/ala An eigenvector of a matrix is a vector v that satisfies Av = Lv. In other words, after A "acts on" the vector v, the result is the vector v just scaled by the constant number L. In this example, we find the eigenvectors of a given 3x3 matrix. This is done by finding the null space of the matrix A-LI. The null space solution (A-LI)x = 0 always results in an infinite number of solutions for the vector x. As such, we find a basis for each one of these solutions, and thus the "basis for an eigenspace" terminology. If you enjoyed my videos please "Like", "Subscribe", and visit http://adampanagos.org to setup your member account to get access to downloadable slides, Matlab code, an exam archive with solutions, and exclusive members-only videos. Thanks for watching!