Rank nullity theorem | Linear Transformation | Part 1

🎓 VTU 1BMATS101 (2025 Scheme) | Linear Transformations | Module 5 🎓 VTU BMATS201 (Module 3) & BMATE201 (Module 2) | Vector Space & Linear Transformations | 2022 Scheme ━━━━━━━━━━━━━━━━━━━━━━ 📌 Question Covered Find the range, null space, rank, and nullity of the transformation T : V3(R) → V2(R) defined by T(x, y, z) = (y − x, y − z). Also verify the Rank–Nullity Theorem for the given transformation. This problem is solved step by step by: • Finding the null space of T • Determining the range of T • Computing rank and nullity • Verifying that rank(T) + nullity(T) = dimension of V3(R) The explanation is systematic, concept-based, and strictly exam-oriented, making it suitable for VTU Model Question Papers and Semester Examinations. ━━━━━━━━━━━━━━━━━━━━━━ 🆕 NEW – VTU 1BMATS101 (2025 Scheme) (Most Important) 📘 Module 1 – Calculus 👉    • Calculus | VTU 1BMATS101 – Module 1 (Semes...   📘 Module 3 – Linear Algebra 👉    • Linear Algebra Made Simple – Complete   ━━━━━━━━━━━━━━━━━━━━━━ 📚 All 1BMATS101 Playlists 👉 Model QP–I (2025)    • 1BMATS101 | VTU Calculus & Linear Algebra ...   👉 Module 1    • Partial Differentiation | Multivariable Ca...   👉 Module 2    • Vector Calculus | VTU 1BMATS101 – Module 2...   👉 Module 3    • Linear Algebra: System of Equations & Eige...   👉 Module 4    • Vector Space | VTU 1BMATS101 – Module 4 (S...   👉 Module 5    • Linear Transformation | VTU 1BMATS101 – Mo...   ━━━━━━━━━━━━━━━━━━━━━━ 📘 Reference: Module-wise VTU Question Solutions 📘 Module 1 | Calculus Q1(a) Partial Differentiation –    • Partial differentiation engineering mathem...   Q1(b) Jacobian –    • Jacobian engineering mathematics   Q1(c) Maxima & Minima –    • Maxima and minima engineering mathematics    Q2(a) Chain Rule –    • Chain rule of partial differentiation   Q2(b) Jacobian –    • Jacobian   Q2(c) Maclaurin Series –    • maclaurin series of two variables   📘 Module 2 | Vector Calculus Q3(a) Gradient –    • Vector calculus | Gradient of Dot Product   Q3(b) Irrotational Field –    • Vector calculus engineering mathematics | ...   Q3(c) Spherical Coordinates –    • cartesian to spherical coordinates | vecto...   Q4(a) Directional Derivative –    • Vector calculus engineering mathematics | ...   Q4(b) Divergence & Curl –    • Vector calculus engineering mathematics | ...   Q4(c) Cylindrical Coordinates –    • Cartesian to cylindrical coordinates | Vec...   📘 Module 3 | Linear Systems & Eigenvalues Q5(a) Rank –    • Rank of matrix | Linear algebra    Q5(b) Diagonalization –    • Diagonalization of Matrices | Linear Algebra   Q5(c) Traffic Flow –    • Traffic flow linear algebra   Q6(a) Consistency –    • Test for consistency and solve the equatio...   Q6(b) Gauss–Jordan –    • Gauss Jordan Method   Q6(c) Eigenvalues –    • Eigen values & eigen vectors    📘 Module 4 | Vector Space Q7(a) Linear Combination –    • Linear combination of the vector | Vector ...   Q7(b) Subspace –    • Subspace of r3 | Vector space   Q7(c) Basis of Spaces –    • Basis dimension row space column space nul...   Q8(a) Basis & Dimension –    • Basis and dimension of a vector space | Ve...   Q8(b) Inner Product –    • Inner product in vector space | Vector space   Q8(c) Coordinates w.r.t. Basis –    • Vector Space | Coordinates of a vector wit...   ━━━━━━━━━━━━━━━━━━━━━━ 👉 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 for exclusive perks 👇 🔗    / @officialmathematicstutor   ━━━━━━━━━━━━━━━━━━━━━━ #LinearTransformation #VectorSpace #1BMATS101 #VTUMaths #LinearAlgebra #EngineeringMathematics #VTUExamPreparation .