Find Aⁿ Using Diagonalisation | Eigenvalues & Eigenvectors

Welcome to MathLadder! 📚✨ In this video, we learn how to find the power of a matrix (Aⁿ) using diagonalisation. The method is explained step by step using eigenvalues, eigenvectors, and diagonal matrices. Instead of multiplying the matrix repeatedly, diagonalisation provides a systematic way to calculate higher powers of a matrix easily. 📌 Topics Covered: • Matrix powers and finding Aⁿ • Diagonalisation of a matrix • Finding eigenvalues • Finding eigenvectors • Forming the modal matrix P • Finding P⁻¹ • Using A = PDP⁻¹ • Calculating Aⁿ using diagonalisation • Step-by-step solved example • Important exam tips 🎓 Useful for: Engineering Mathematics | Linear Algebra | Matrices | Eigenvalues | Eigenvectors | Matrix Diagonalisation | Matrix Powers 🔔 Subscribe to MathLadder for more mathematics tutorials, concepts, and step-by-step problem solving. 👍 Like | 💬 Comment | 📤 Share | 🔔 Subscribe #MathLadder #MatrixPower #Diagonalisation #MatrixDiagonalisation #Eigenvalues #Eigenvectors #Matrices #LinearAlgebra #EngineeringMathematics #MathsTutorial