Eigenvalues and Eigenvectors of a 2 by 2 Matrix

The video starts with the necessary definitions of parallel vectors and the eigenvalues and eigenvectors using numerical examples. Then the calculations start with the main equation of eigenvectors: AX = Lambda X. The condition of the determinant of the matrix A - Lambda I being equal to zero leads to the characteristic equation which when solved gives solutions called the eigenvalues. With the knowledge of the eigenvalues, the eigenvectors are then calculated. We go even further and check that one eigenvector and its corresponding eigenvalue satisfies the equation: AX - Lambda X. This video gives a truly deep analysis of the concept and the calculation skills of eigenvectors and eigenvalues. More at https://www.analyzemath.com/linear-algebra.html More at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 12 math practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1