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Full Example: Diagonalizing a Matrix

Let's compute a full example of Diagonalizing a matrix via eigenvectors and eigenvalues. The steps: 1) Compute the eigenvalues. Take the determinant of A-lambda I and set it equal to zero. The solutions are the eigenvalues 2) Compute the eigenvectors. For each eigenvalue solve (A-lambda I)x=0, which is a homogeneous system 3) Form the P and D matrix. The D matrix is just the eigenvalues down the main diagonal. The P matrix is the corresponding linearly independent eigenvectors for each eigenvalue as columns, in the same order as their eigenvalues were put into D. 4) Finally, we can test that A=PDP^-1 is true by multiplying out the right hand side. How to VISUALIZE the diagonalization process:    • Visualizing Diagonalization & Eigenbases   How to COMPUTE the diagonalization proces:    • How the Diagonalization Process Works   BECOME A MEMBER: ►Join:    / @drtrefor   MATH BOOKS I LOVE (affilliate link): ► https://www.amazon.com/shop/treforbazett COURSE PLAYLISTS: ►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Log...   ►LINEAR ALGEBRA:    • Linear Algebra (Full Course)   ►CALCULUS I:    • Calculus I (Limits, Derivative, Integ...   ► CALCULUS II:    • Calculus II (Integration Methods, Ser...   ►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus ...   ►VECTOR CALCULUS (Calc IV)    • Calculus IV: Vector Calculus (Line In...   ►DIFFERENTIAL EQUATIONS:    • Ordinary Differential Equations (ODEs)   ►LAPLACE TRANSFORM:    • Laplace Transforms and Solving ODEs   ►GAME THEORY:    • Game Theory   OTHER PLAYLISTS: ► Learning Math Series    • 5 Tips To Make Math Practice Problems...   ►Cool Math Series:    • Cool Math Series   SOCIALS: ►X/Twitter: http://X.com/treforbazett ►TikTok:   / drtrefor   ►Instagram (photography based):   / treforphotography