JEE ADVANCED : Diagonalization of 3×3 Complex Matrices Made EASY скачать в хорошем качестве

JEE ADVANCED : Diagonalization of 3×3 Complex Matrices Made EASY

#IITJEEmaths #eigenvaluesandeigenvectors #linearalgebra #mathsolympiad #rankofmatrix #eigenvectors #3x3MatrixEigenvalues #rmo #complexmatrix #iitianexplains #diagonalization #matrixexplained #csirnetmaths #matrixalgebra #MATHS&SCIENCE BY IITIAN In this video for JEE Mains & JEE ADVANCED , CSIR maths aspirants, : Diagonalization of 3×3 Complex Matrices Made EASY by an IITian. Complete solution of a challenging 3×3 complex matrix problem with alternating (1+i) and (1-i) elements, where one eigenvalue λ₃=0 is given. Perfect for IIT JEE Advanced, CSIR NET, GATE Mathematics aspirants. 📌 Problem Statement: Find eigenvalues and eigenvectors for: text A = [ 1+i 1-i 1+i ] [ 1-i 1+i 1-i ] [ 1+i 1-i 1+i ] Given: λ₃ = 0 🎯 What You’ll Learn: ✅ Step 1: Recognize matrix structure – alternating complex entries, repeated rows/columns ✅ Step 2: Find λ=0 eigenvector instantly using row dependency ✅ Step 3: Assume eigenvector form (x, y, x) – reduces 3D to 2D system ✅ Step 4: Solve quadratic for eigenvalues λ₁, λ₂ using trace condition ✅ Step 5: Complete diagonalization – find all 3 eigenvectors explicitly Chapter Coverage (IIT JEE/CSIR NET): Linear Algebra Eigenvalues & Eigenvectors Complex Matrices Matrix Diagonalization Rank & Nullity Applications Why This Problem is Important: 🔥 IIT JEE Advanced: Repeated pattern in complex matrix problems 🔥 CSIR NET/GATE: Tests conceptual clarity in eigenvector computation 🔥 Common Trick: Spotting symmetric structure reduces calculation time 🔥 Exam Shortcut: Eigenvectors of form (x, y, x) for this matrix type 📝 Complete Solution Summary: Eigenvalues: λ₁ = (3+√7)/2 + i(3-√7)/2 λ₂ = (3-√7)/2 + i(3+√7)/2 λ₃ = 0 Eigenvectors: v₁ = [1, (√7-i)/2, 1]ᵀ v₂ = [1, (-√7-i)/2, 1]ᵀ v₃ = [1, 0, -1]ᵀ Diagonalization: A = P D P⁻¹ where D = diag(λ₁, λ₂, 0) Subscribe to my channel MATHS & SCIENCE BY IITIAN. Hit 🔔 to never miss a problem that looks easy but tests deep insight. The playlists and links for all videos are given as below: MATHEMATICS BY IITIAN    • MATHEMATICS BY  IITIAN   Channel Name: MATHS & SCIENCE BY IITIAN Handle: @mathsciencebyiitian Email: mathsisscience@gmail.com Kindly view, review, and comment on videos for improvement, and subscribe to my channel.