linear dependence and independence of vectors | Vector Space | Part 16

Описание: Vector Space | VTU 1BMATS101 – Module 4 (Semester 1 Engineering Mathematics):    • Vector Space | VTU 1BMATS101 – Module 4 (S...  

🎯 Check Whether Vectors Form a Basis Using Row Echelon Form

🧮 Question:
Determine whether following set of vectors (5, 3, 7, 4), (3, 26, 2, 9), (7, 2, 10, 5) form a basis of a vector space


📘 Concept Covered:
Basis of a Vector Space
Using Row Echelon Form to test for linear dependence

📚 Chapter:
Vector Space and Linear Transformation

📚 This topic is important for the following VTU subject codes:
🔹 1BMATS101 – Module 4 (CSE/ISE)
🔹 BMATS201 – Module 3 (CSE/ISE)
🔹 BMATE201 – Module 2 (EEE/ECE)
🔹 BCS405D – Module 1 (2nd Year CSE – Linear Algebra)


📽️ Watch the full video to understand this step-by-step method clearly

📺 Video-wise List (Module 4)

Part 1 – Linear Combination of Vectors
Question: Identify which vectors are linear combinations of given vectors
Link:    • Linear Combination of Vectors | Vector Spa...  

Part 2 – Linear Combination of Vectors
Question: Show (5,9,5) is a linear combination of three vectors
Link:    • Linear Combination of Vectors | Vector Spa...  

Part 3 – Linear Span of Vectors
Question: Verify whether (2,2,3) lies in the span of given vectors
Link:    • Linear Span of Vectors | Vector Space | Pa...  

Part 4 – Linear Combination with Parameter
Question: Find k such that (1,−2,k) is a linear combination
Link:    • Linear Combination of Vectors | Vector Spa...  

Part 5 – Linear Span (Not in Span)
Question: Show (5,9,5) is not in the span of given set
Link:    • Linear Span of Vectors | Vector Space | Pa...  

Part 6 – Linear Combination of Polynomials
Question: Express a polynomial as a linear combination
Link:    • Linear Combination of Polynomials | Vector...  

Part 7 – Linear Combination of Matrices
Question: Check whether a matrix is a linear combination
Link:    • Linear Combination of Matrices | Vector Sp...  

Part 8 – Linear Span of R3
Question: Check whether given vectors span R3
Link:    • linear span of a vector space | Vector Spa...  

Part 9 – Linear Span Proof
Question: Prove vectors span R3
Link:    • linear span of a vector space | Vector Spa...  

Part 10 – Polynomial in Span
Question: Show polynomial lies in span of given polynomials
Link:    • Linear Combination of Polynomials | Vector...  

Part 11 – Linear Independence
Question: Check independence of two vector sets
Link:    • linear dependence and independence of vect...  

Part 12 – Linear Dependence
Question: Show a given set is linearly dependent
Link:    • linear dependence and independence of vect...  

Part 13 – Dependence of Two Sets
Question: Prove both sets are linearly dependent
Link:    • linear dependence and independence of vect...  

Part 14 – Linear Dependence Test
Question: Check whether given set is dependent
Link:    • linear dependence and independence of vect...  

Part 15 – Basis Check
Question: Determine whether vectors form a basis
Link:    • linear dependence and independence of vect...  

Part 16 – Basis in R4
Question: Check whether given vectors form a basis
Link:    • linear dependence and independence of vect...  

Part 17 – Basis and Dimension
Question: Find basis and dimension of a subspace
Link:    • Basis and dimension of a vector space | Ve...  

Part 18 – Basis and Dimension
Question: Find basis and dimension (4 vectors)
Link:    • Basis and dimension of a vector space | Ve...  

Part 19 – Basis and Dimension
Question: Find basis and dimension of given vectors
Link:    • Basis and dimension of a vector space | Ve...  

Part 20 – Basis and Dimension
Question: Find basis and dimension of subspace
Link:    • Basis and dimension of a vector space | Ve...  

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🆕 NEW – 1BMATS101 Module 1 Playlist (2025 Scheme)
Calculus | VTU 1BMATS101 – Module 1
👉    • Calculus | VTU 1BMATS101 – Module 1 (Semes...  

🆕 NEW – 1BMATS101 Module 3 Playlist (2025 Scheme)
Module 3 – Linear Algebra Made Simple:    • Linear Algebra Made Simple – Complete  


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📌 All 1BMATS101 Playlists • Model Question Paper–I (2025):    • 1BMATS101 | VTU Calculus & Linear Algebra ...  
• Module 1 – Partial Differentiation (NEW):    • Partial Differentiation | Multivariable Ca...  
• Module 2 – Vector Calculus:    • Vector Calculus | VTU 1BMATS101 – Module 2...  
• Module 3 – Linear Algebra:    • Linear Algebra: System of Equations & Eige...  
• Module 4 – Vector Space :    • Vector Space | VTU 1BMATS101 – Module 4 (S...  
• Module 5 – Linear Transformation:    • Linear Transformation | VTU 1BMATS101 – Mo...  

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