Linear vs Non-Linear Transformations | Why One Has a Constant Term

Understand the difference between Linear and Non-Linear Transformations with an important VTU exam question, explained step-by-step. Perfect for BCS405D and 1BMATS101 students to clearly identify linearity using standard conditions. ━━━━━━━━━━━━━━━━━━━━━ 📌 Exact Question: ❓ If S and T are transformations from V₂(R) to V₂(R) defined by S(x, y) = (3x + 2y, 3x − 4y) T(x, y) = (x + 3, y − 2), show that S is a linear transformation but T is not a linear transformation. ━━━━━━━━━━━━━━━━━━━━━ 🎯 Learning Points: ✔ Conditions for linear transformation ✔ Additivity and homogeneity test ✔ Constant term → non-linear case ✔ Quick exam shortcut method ✔ Concept clarity with comparison ━━━━━━━━━━━━━━━━━━━━━ 📚 Watch Next: 1️⃣ Basic Linear Transformation https://youtu.be/G6QoFz7rWMs 2️⃣ Rank & Nullity (Core Concept) https://youtu.be/0SoG__eh7_M 3️⃣ Full Playlist (Start from beginning) https://www.youtube.com/playlist?list=PLM9RnGtTy9_9lAWtTqWSNXi4ApcJUQx7k ━━━━━━━━━━━━━━━━━━━━━ 📘 Module Playlist (Start to Finish): ▶️ BCS405D – Module 2 (Linear Transformations) https://www.youtube.com/playlist?list=PLM9RnGtTy9_9lAWtTqWSNXi4ApcJUQx7k ▶️ 1BMATS101 – Module 5 (Linear Transformation) https://www.youtube.com/playlist?list=PLM9RnGtTy9__fllLHI_SsGvlsurgj-BjE ━━━━━━━━━━━━━━━━━━━━━ 📙 More Practice / Related Topics: 1️⃣ Vector Spaces https://www.youtube.com/playlist?list=PLM9RnGtTy9_9ybQUjtwVyix1Acy6B7eiG 2️⃣ Eigenvalues & Eigenvectors https://www.youtube.com/playlist?list=PLM9RnGtTy9_82B3CoOgAnhaV9V5mj2WI2 3️⃣ Inner Product Spaces https://www.youtube.com/playlist?list=PLM9RnGtTy9_-SUY_ZFZm_T2O9ofIOB3og ━━━━━━━━━━━━━━━━━━━━━ 🚀 Next Step: Move to transformations between different dimensions. 📌 Don’t stop here: Practice identifying linear vs non-linear quickly. ━━━━━━━━━━━━━━━━━━━━━ 📘 Subject Details: 📚 Subject Codes: • BCS405D – Linear Algebra • 1BMATS101 – Calculus & Linear Algebra 📌 Topic: Linear Transformations ━━━━━━━━━━━━━━━━━━━━━ 📙 All Playlists (VTU Maths): ▶️ 1BMATS101 – Model Question Papers https://www.youtube.com/playlist?list=PLM9RnGtTy9_9LJxGYqFDpMOlhwYivpCAN ▶️ 1BMATS101 – Module 1 (Calculus) https://www.youtube.com/playlist?list=PLM9RnGtTy9_-rqPtcCwDq2MBKGy4pDk6K ▶️ 1BMATS101 – Module 2 (Vector Calculus) https://www.youtube.com/playlist?list=PLM9RnGtTy9_9CcDmlQM7n_q6ABPHD5As- ▶️ 1BMATS101 – Module 3 (Linear Algebra) https://www.youtube.com/playlist?list=PLM9RnGtTy9_-rSzBJZDttMpYRKQYzxTm4 ▶️ 1BMATS101 – Module 4 (Vector Space) https://www.youtube.com/playlist?list=PLM9RnGtTy9_88Z1aKoF-xcrhEZ3Z4ElAB ▶️ 1BMATS101 – Module 5 (Linear Transformation) https://www.youtube.com/playlist?list=PLM9RnGtTy9__fllLHI_SsGvlsurgj-BjE ━━━━━━━━━━━━━━━━━━━━━ ▶️ BCS405D – Module 1 (Vector Spaces) https://www.youtube.com/playlist?list=PLM9RnGtTy9_9ybQUjtwVyix1Acy6B7eiG ▶️ BCS405D – Module 2 (Linear Transformations) https://www.youtube.com/playlist?list=PLM9RnGtTy9_9lAWtTqWSNXi4ApcJUQx7k ▶️ BCS405D – Module 3 (Eigenvalues & Eigenvectors) https://www.youtube.com/playlist?list=PLM9RnGtTy9_82B3CoOgAnhaV9V5mj2WI2 ▶️ BCS405D – Module 4 (Inner Product Spaces) https://www.youtube.com/playlist?list=PLM9RnGtTy9_-SUY_ZFZm_T2O9ofIOB3og ▶️ BCS405D – Module 5 (Optimization Techniques) https://www.youtube.com/playlist?list=PLM9RnGtTy9__Xai2X0_I5mcu5v8jJkaqr ━━━━━━━━━━━━━━━━━━━━━ 👉 Follow VTU Maths with Muheeb (Mathematics Tutor) on WhatsApp https://whatsapp.com/channel/0029Vb6ct0L30LKOlXViVx3Y 👉 Get all VTU Maths updates and video links on Telegram https://t.me/vtumathswithmathematicstutor 💎 Support Us: Join our channel and get access to exclusive perks 👇 https://www.youtube.com/channel/UC_OTtwh8_-q-bA7DoS--syg/join ━━━━━━━━━━━━━━━━━━━━━ #LinearTransformation #LinearAlgebra #VTUMaths #BCS405D #1BMATS101 #EngineeringMaths #NonLinear