Gauss Jordan Method

📘 Gauss Jordan Method | System of Linear Equations | VTU 1BMATS101

📝 Question Discussed in the Video
VTU Model Question Paper–I (2025 Scheme)
Subject Code: 1BMATS101 – Calculus & Linear Algebra
Module: 3 – Linear Algebra
Question No.: 6(b)

Question:
Apply Gauss–Jordan method to approximate the solutions of the system
83x + 11y − 4z = 95
7x + 52y + 13z = 104
3x + 8y + 29z = 71

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📘 Module 1 | Calculus | VTU 1BMATS101 (2025 Scheme)

1️⃣ Partial Differentiation | Q 1(a)
Question:
Prove that ∂u/∂x + ∂u/∂y = u,
when u = e^(x+y) / [(e^x)(e^y)].
👉 https://youtu.be/E6mulwLxBLM

2️⃣ Jacobian | Q 1(b)
Question:
If u = x + 3y² − z³, v = 4x²yz, w = 2z² − xy,
find ∂(u,v,w)/∂(x,y,z) at (1, −1, 0).
👉 https://youtu.be/GArSusUlIFM

3️⃣ Maxima and Minima | Q 1(c)
Question:
Find the extreme values of
f(x,y) = xy + a³/x + a³/y.
👉 https://youtu.be/4hRGFt34r2o

4️⃣ Chain Rule | Q 2(a)
Question:
If v = f(r,s,t), r = x/y, s = y/z, t = z/x,
show that x(∂v/∂x)+y(∂v/∂y)+z(∂v/∂z)=0.
👉 https://youtu.be/62iktdBCZwE

5️⃣ Jacobian | Q 2(b)
Question:
If u = 2yz/x, v = 3zx/y, w = 4xy/z,
find ∂(u,v,w)/∂(x,y,z).
👉 https://youtu.be/xx6z6jsJTyU

6️⃣ Maclaurin Series | Q 2(c)
Question:
Expand cos x · cos y using Maclaurin’s series
up to second-degree terms.
👉 https://youtu.be/4TNwD_DT89M

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📘 Module 2 | Vector Calculus | VTU 1BMATS101 (2025 Scheme)

1️⃣ Gradient of Dot Product | Q 3(a)
Question:
If f = x²yz and g = xy − 3z², calculate ∇(∇f • ∇g).
👉 https://youtu.be/RqZ2_HRjYx8

2️⃣ Irrotational Field & Scalar Potential | Q 3(b)
Question:
Given f = (6xy + z³)i + (3x² − z)j + (3xz² − y)k,
show that the field is irrotational and find its scalar potential.
👉 https://youtu.be/v47Dx4c5rDc

3️⃣ Cartesian to Spherical Coordinates | Q 3(c)
Question:
Express the vector F⃗ = x î + 2y ĵ + yz k̂
in spherical polar coordinates.
👉 https://youtu.be/0ApeNnO3rAU

4️⃣ Directional Derivative | Q 4(a)
Question:
Find the directional derivative of
f(x,y,z) = 4e^(2x − y + z)
at (1,1,−1) in the direction towards (−3,5,6).
👉 https://youtu.be/zhetMtjwl2I

5️⃣ Divergence & Curl | Q 4(b)
Question:
Find the divergence and curl of vector f, where
f = grad(x³ + y³ + z³ − 3xyz).
👉 https://youtu.be/WMUuzV4b3Ng

6️⃣ Cartesian to Cylindrical Coordinates | Q 4(c)
Question:
Express the vector F⃗ = 2x î + 3y ĵ − z k̂
in cylindrical polar coordinates.
👉 https://youtu.be/1wfTmva0PL8

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📘 Module 3 | System of Linear Equations, Eigenvalues and Eigenvectors | VTU 1BMATS101 (2025 Scheme)

Part 1 👉 Rank of Matrix | Q 5(a)
Find constant b if rank of a 4×4 matrix is 3
https://youtu.be/iLt6QxLqQwI

Part 2 👉 Diagonalization of Matrix | Q 5(b)
Find modal matrix and verify diagonalization
https://youtu.be/dMMtsZBicgw

Part 3 👉 Traffic Flow Problem | Q 5(c)
Form and solve system of linear equations
https://youtu.be/_F9uXRQjsMA

Part 4 👉 Test for Consistency | Q 6(a)
Investigate values of λ and μ
https://youtu.be/OwSTVeavKrg

Part 5 👉 Gauss–Jordan Method | Q 6(b)
Solve system using Gauss–Jordan method
https://youtu.be/f-BAr5fteHU

Part 6 👉 Eigenvalues & Eigenvectors | Q 6(c)
Find eigenvalues and eigenvectors
https://youtu.be/KoJ4sOuRUww

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📘 Module 4 | Vector Space | VTU 1BMATS101 (2025 Scheme)

Part 1 👉 Linear Combination of Vectors (Q.7a)
https://youtu.be/E-4HF7ADWFg

Part 2 👉 Subspace of R3 (Q.7b)
https://youtu.be/MWDwu-KQwKQ

Part 3 👉 Basis & Dimension of Row, Column and Null Space (Q.7c)
https://youtu.be/idatYZKtu2Q

Part 4 👉 Basis & Dimension of a Vector Space (Q.8a)
https://youtu.be/npSwrdUs8sM

Part 5 👉 Inner Product in Vector Space (Q.8b)
https://youtu.be/JTOsSg_5r-Q

Part 6 👉 Coordinates of a Vector w.r.t. a Basis (Q.8c)
https://youtu.be/cmcFtz8yALw

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🆕 NEW – VTU 1BMATS101 (2025 Scheme)

📘 Module 1 – Calculus
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_-rqPtcCwDq2MBKGy4pDk6K

📘 Module 3 – Linear Algebra
👉 https://www.youtube.com/playlist?list=PLM9RnGtTy9_-rmNJXVPre7KSNkYjG63d5

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👉 Module 4: https://www.youtube.com/playlist?list=PLM9RnGtTy9_88Z1aKoF-xcrhEZ3Z4ElAB
👉 Module 5: https://www.youtube.com/playlist?list=PLM9RnGtTy9__fllLHI_SsGvlsurgj-BjE

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