Lec -2 | Matrices | Echelon Form of a Matrix and it's Rank | Two Questions Have Been Solved

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Lecture-2: Echelon Form of a Matrix and it's Rank | Two Questions Have Been Solved
In this lecture, Definition of Echelon form is provided and two questions have been solved for making better understanding

Content:
00:21 : Echelon form of Matrix (Definition and examples)
16: 16 : Rank of the matrix in echelon form (Definition and examples)
21:35 : Question 1 (Detailed solution has been provided)
36:22 : Question 2 (Detailed solution has been provided)

Complete playlist of Matrices 2.0
   • Matrices 2.0  

Lecture 1:
Lecture 2:
Lecture 3:
Lecture 4:

Engineering Mathematics I Mathematics for Undergraduate and Post-Graduate Students I
IIT JAM I GATE I CSIR (NET)

Your Queries:
Matrix
Matrices
Elementary rows and columns transformation
Elementary rows and columns operations
Echelon form of the matrix
Normal form of the matrix
Canonical form of the matrix
Rank of the matrix
Rank of the matrix in Echelon form
Rank of the matrix in Normal form / Canonical form
Inverse of the Matrix by elementary transformations/operations
Rank of matrix by reducing the matrix A into PAQ normal form
PAQ normal form of the matrix
System of simultaneous linear equations
Homogeneous linear equations
Non homogeneous linear equations
No solution, unique solution of equations and infinite solutions
Trivial solution and Non-trivial solutions
zero solution and non zero solutions
Characteristic matrix
Characteristic polynomial
Characteristic equation
Characteristic roots/Eigen values
Characteristic vectors/Eigen vectors
Spectrum
Cayley-Hamilton theorem
Verification of Cayley-Hamilton theorem
Application of Cayley-Hamilton theorem
Linear dependence and linear independence of vectors
Complex matrices
Symmetric and Skew Symmetric matrices
Orthogonal Matrix
Hermitian and Skew Hermitian matrices
Unitary Matrix
Nilpotent matrix
Idempotent Matrix
Rank and Nullity

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Dr. Sanjay Singh