Rank nullity theorem | Linear Transformation | Part 1 скачать в хорошем качестве

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 | Rank, Consist...   ━━━━━━━━━━━━━━━━━━━━━━ 📚 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 | Calculus | VTU 1...   Q1(b) Jacobian –    • Jacobian | Calculus | VTU 1BMATS101 | Q1(b)   Q1(c) Maxima & Minima –    • Maxima and Minima | Calculus | VTU 1BMATS1...   Q2(a) Chain Rule –    • Chain Rule of Partial Differentiation | Ca...   Q2(b) Jacobian –    • Jacobian | Calculus | VTU 1BMATS101 | Q2(b)   Q2(c) Maclaurin Series –    • Maclaurin Series of Two Variables | Calcul...   📘 Module 2 | Vector Calculus Q3(a) Gradient –    • Gradient of Dot Product | Vector Calculus ...   Q3(b) Irrotational Field –    • Irrotational Vector Field and Scalar Poten...   Q3(c) Spherical Coordinates –    • Cartesian to Spherical Polar Coordinates |...   Q4(a) Directional Derivative –    • Directional Derivative | Vector Calculus |...   Q4(b) Divergence & Curl –    • Divergence and Curl | Vector Calculus | VT...   Q4(c) Cylindrical Coordinates –    • Cartesian to Cylindrical Polar Coordinates...   📘 Module 3 | Linear Systems & Eigenvalues Q5(a) Rank –    • Rank of Matrix | Linear Algebra | VTU 1BMA...   Q5(b) Diagonalization –    • Diagonalization of Matrix (Modal Matrix) |...   Q5(c) Traffic Flow –    • Traffic Flow Problem | Linear Algebra | VT...   Q6(a) Consistency –    • Test for Consistency of Linear Equations |...   Q6(b) Gauss–Jordan –    • Gauss Jordan Method | Linear Algebra | VTU...   Q6(c) Eigenvalues –    • Eigenvalues and Eigenvectors | Linear Alge...   📘 Module 4 | Vector Space Q7(a) Linear Combination –    • Linear Combination of Vectors | Vector Spa...   Q7(b) Subspace –    • Subspace Test | Vector Space | VTU 1BMATS1...   Q7(c) Basis of Spaces –    • Basis and Dimension of Row Space, Column S...   Q8(a) Basis & Dimension –    • Basis and Dimension of a Subspace | Vector...   Q8(b) Inner Product –    • Inner Product of Vectors | Vector Space | ...   Q8(c) Coordinates w.r.t. Basis –    • Coordinates of a Vector with Respect to a ...   ━━━━━━━━━━━━━━━━━━━━━━ 👉 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 .