🔥Diagonalizability of Matrices | CSIR NET Mathematical Sciences | Linear Algebra PYQ with Theory

In this video, we break down one of the most frequently asked and high-scoring topics in CSIR NET Linear Algebra: Diagonalizability of Matrices. Learn how to determine if a matrix is diagonalizable over R in under 60 seconds without wasting time computing full eigenvectors. We cover the core theory of Algebraic Multiplicity (AM) vs. Geometric Multiplicity (GM), the Rank-Nullity shortcut, and solve a classic CSIR NET previous year question step-by-step. 📌 Key Takeaways: 1. Field condition for eigenvalues (R vs C). 2. Shortcut formula: GM(λ) = n - Rank(A - λI). 3. Fast option elimination technique for Part B and Part C questions. ⏱️ Timestamps: 0:00 - Introduction & The Question 0:45 - Core Theory: AM vs GM & Rank Shortcut 2:30 - Eliminating Option (A) [Field Check] 3:35 - Eliminating Option (B) [Repeated Eigenvalue Check] 4:30 - Eliminating Option (D) [Rank Analysis] 5:10 - Verifying Option (C) [Why AM = GM] 5:45 - Golden Rules & Common Traps to Avoid 7:00 - Practice Question for You (Comment your answer!) ✍️ Practice Question: Is the matrix M = [[3, 0, 0], [0, 3, 1], [0, 0, 3]] diagonalizable over R? Drop your answer (YES or NO) with your reasoning in the comments below! 🔔 Subscribe to The Pure Intuition for conceptual clarity, proof intuitions, and problem-solving shortcuts for CSIR NET, IIT JAM, and GATE Mathematics. #CSIRNET #LinearAlgebra #Mathematics #CSIRNETMaths #ThePureIntuition #HigherMathematics #IITJAMMaths #GATEMaths #linearalgebra #csirnet #csirnetmaths #highermathematics #mathematics #gatemaths #iitjam #mathstricks #iitjammaths