QR decomposition | Linear Algebra | Part 1

Master QR Decomposition with an important VTU exam question explained step-by-step. Perfect for BCS405D students to understand how to decompose a matrix into orthogonal and upper triangular matrices. ━━━━━━━━━━━━━━━━━━━━━ 📌 Exact Question: ❓ Obtain the Q R decomposition of 3×3 matrix contains 1st column 1 1 1 2nd column 0 1 1 3rd column 0 0 1 ━━━━━━━━━━━━━━━━━━━━━ 🎯 Learning Points: ✔ Concept of QR Decomposition ✔ Relation with Gram-Schmidt process ✔ Constructing Q (orthonormal matrix) ✔ Constructing R (upper triangular matrix) ✔ Checking possibility of decomposition ✔ Exam-oriented solving method ━━━━━━━━━━━━━━━━━━━━━ 📚 Watch Next (Simple Chain): 1️⃣ Matrix Gram-Schmidt    • Gram-Schmidt on 3×3 Matrices | Complete Pr...   2️⃣ QR Decomposition (Next Variation)    • QR Decomposition in 10 Minutes | Linear Al...   3️⃣ QR Decomposition (2×2 Case)    • 2×2 Matrix QR Decomposition | Fastest Meth...   ━━━━━━━━━━━━━━━━━━━━━ 📘 Module Playlist (Start to Finish): ▶️ BCS405D – Module 4 (Inner Product Spaces)    • Gram Schmidt & QR Decomposition Made Easy ...   ━━━━━━━━━━━━━━━━━━━━━ 📙 More Practice / Related Method: 1️⃣ Gram-Schmidt Basics    • Convert Any Basis to Orthogonal Basis | Gr...   2️⃣ Orthonormal Basis    • Gram Schmidt Orthonormalization | R³ Ortho...   ━━━━━━━━━━━━━━━━━━━━━ 🚀 Next Step: Move to more QR decomposition variations. 📌 Don’t stop here: Practice QR decomposition repeatedly. ━━━━━━━━━━━━━━━━━━━━━ 📘 Subject Details: 📚 Subject Code: • BCS405D – Linear Algebra 📌 Topic: Inner Product Spaces ━━━━━━━━━━━━━━━━━━━━━ 📙 All Playlists (BCS405D): ▶️ Module 1 – Vector Spaces    • BCS405D Module-1: VECTOR SPACES   ▶️ Module 2 – Linear Transformations    • BCS405D Module-2: LINEAR TRANSFORMATIONS   ▶️ Module 3 – Eigenvalues & Eigenvectors    • BCS405D Module-3: EIGENVALUES AND EIGENVEC...   ▶️ Module 4 – Inner Product Spaces    • Gram Schmidt & QR Decomposition Made Easy ...   ▶️ Module 5 – Optimization Techniques    • BCS405D Module-5: OPTIMIZATION TECHNIQUES ...   ━━━━━━━━━━━━━━━━━━━━━ 👉 Follow VTU Maths with Muheeb (Mathematics Tutor) on WhatsApp https://whatsapp.com/channel/0029Vb6c... 👉 Get all VTU Maths updates and video links on Telegram https://t.me/vtumathswithmathematicst... 💎 Support Us: Join our channel and get access to exclusive perks 👇    / @officialmathematicstutor   ━━━━━━━━━━━━━━━━━━━━━ #QRDecomposition #GramSchmidt #LinearAlgebra #BCS405D #VTUMaths #InnerProductSpaces #EngineeringMaths