Gauss–Seidel Iteration Method | Q9(b) | Model Paper-I 2025 | VTU 1BMATE101

Описание: 📘 VTU Model Question Paper–I (2025 Scheme)
1BMATE101 – Differential Calculus & Linear Algebra
First Semester B.E./B.Tech

📍 Module-5: Linear Algebra

📝 Question No. 9(b)

📘 Gauss–Seidel Iteration Method | Numerical Methods | VTU Exam Problem

In this video, we solve a VTU Numerical Methods problem using the Gauss–Seidel Iteration Method to find the solution of a system of linear equations.

📄 Problem Statement
Solve the following system of linear equations using the Gauss–Seidel iteration method:
20x + y − 2z = 17
3x + 20y − z = −18
2x − 3y + 20z = 25

📘 VTU Model Question Paper–I 2025
1BMATE101 – Differential Calculus & Linear Algebra
🎓 VTU 2025 Scheme | Semester 1
🔥 MODEL QUESTION PAPER – I (Complete Solved Playlist)
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📍 MODULE 1 – Differential Calculus 📐✍️
Q1(a)
📌 Relation Between Radius Vector and Tangent | Polar Curves
👉    • Relation Between Radius Vector & Tangent |...  
Q1(b)
📌 Angle Between Two Polar Curves
📘 r = a log θ & r = a / log θ
👉    • Angle Between Polar Curves (log θ) | Q1(b)...  
Q1(c)
📌 Radius of Curvature | Trigonometric Curve
👉    • Radius of Curvature Trigonometric Curve | ...  
Q2(a)
📌 Pedal Equation – Derivation | Polar Coordinates
👉    • Pedal Equation Derivation (Polar) | Q2(a) ...  
Q2(b)
📌 Angle of Intersection of Polar Curves
👉    • Angle of Intersection of Polar Curves | Q2...  
Q2(c)
📌 Radius of Curvature Using Pedal Form
👉    • Radius of Curvature Using Pedal Form | Q2(...  
━━━━━━━━━━━━━━━━━━━━━━━
📍 MODULE 2 – Power Series, Limits & Multivariable Calculus 🔁📊
Q3(a)
📌 Maclaurin Series – log(sec x)
👉    • Maclaurin Series log(sec x) | Q3(a) | Mode...  
Q3(b)
📌 Composite Function | Chain Rule
👉    • Chain Rule Partial Derivatives Proof | Q3(...  
Q3(c)
📌 Maxima and Minima of Two Variables
👉    • Maxima & Minima of Function | Q3(c) | Mode...  
Q4(a)
📌 L’Hospital Rule | Indeterminate Forms
👉    • L’Hospital Rule Limit Problem | Q4(a) | Mo...  
Q4(b)
📌 Jacobian | Multivariable Calculus
👉    • Jacobian ∂(x,y,z)/∂(u,v,w) | Q4(b) | Model...  
Q4(c)
📌 L–R Circuit | Application of DE
👉    • L–R Circuit Differential Equation | Q4(c) ...  
━━━━━━━━━━━━━━━━━━━━━━━
📍 MODULE 3 – Ordinary Differential Equations 🔄📐
Q5(a)
📌 Reducible to Exact Differential Equation
👉    • First Order DE (Reducible to Exact) | Q5(a...  
Q5(b)
📌 Differential Equation Solvable for p
👉    • Differential Equation Solvable for p | Q5(...  
Q6(a)
📌 Exact Differential Equation
👉    • Exact Differential Equation Problem | Q6(a...  
Q6(b)
📌 Orthogonal Trajectories
👉    • Orthogonal Trajectories (Parabola) | Q6(b)...  
Q6(c)
📌 Reducible to Clairaut’s Form
👉    • Reducible to Clairaut’s Form | Q6(c) | Mod...  
━━━━━━━━━━━━━━━━━━━━━━━
📍 MODULE 4 – Higher Order Differential Equations ➕📘
Q7(a)
📌 Higher Order Linear Differential Equation
👉    • Higher Order Linear DE Operator Method | Q...  
Q7(b)
📌 Variation of Parameters Method
👉    • Variation of Parameters Method | Q7(b) | M...  
Q7(c)
📌 Cauchy–Euler Differential Equation
👉    • Cauchy–Euler Differential Equation | Q7(c)...  
Q8(a)
📌 Non-Homogeneous Linear DE | Operator Method
👉    • Non-Homogeneous Linear DE | Q8(a) | Model ...  
Q8(b)
📌 Legendre Type Differential Equation
👉    • Legendre Differential Equation | Q8(b) | M...  
━━━━━━━━━━━━━━━━━━━━━━━
📍 MODULE 5 – Linear Algebra 🧮📐
Q9(b)
📌 Gauss–Seidel Iteration Method
👉    • Gauss–Seidel Iteration Method | Q9(b) | Mo...  
Q9(c)
📌 Rayleigh’s Power Method
👉    • Rayleigh Power Method Eigenvalue | Q9(c) |...  
Q10(a)
📌 Consistency of Linear Equations
👉    • Consistency of Linear Equations | Q10(a) |...  
Q10(c)
📌 Eigenvalues and Eigenvectors
👉    • Eigenvalues & Eigenvectors (Matrix Method)...  
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📕 MODULE-WISE REVISION PLAYLISTS 📚
🔥 MODULE 1 – Differential Calculus
👉    • Module 1 Differential Calculus | Polar Cur...  
👉    • Differential Calculus | VTU 1BMATE101 – Mo...  
🔥 MODULE 2 – Power Series & Multivariable Calculus
👉    • Partial Differentiation | Multivariable Ca...  
👉    • Maclaurin’s Series Expansion | Important V...  
👉    • Maclaurin Series Important Problems  
👉    • Indeterminate Forms (1^∞) – Most Important...  
👉    • Power Series, Indeterminate Forms & Multiv...  
🔥 MODULE 3 – Ordinary Differential Equations
👉    • Ordinary Differential Equations (ODE) | VT...  
👉    • Solvable for P (Differential Equations)  
👉    • Ordinary Differential Equations (ODE) of f...  
🔥 MODULE 4 – Higher Order ODE
👉    • Higher-Order Ordinary Differential Equatio...  
🔥 MODULE 5 – Linear Algebra
👉    • Linear Algebra Made Simple | Rank, Consist...  
👉    • Gauss Seidel method and Rayleigh power method  
👉    • Linear Algebra | VTU 1BMATE101 – Module 5 ...  
📌 Note: Gauss–Jordan Method is NOT required for this syllabus.
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