Linear Algebra Part 3 (Row Space & Column space of Matrix)

Basis And Dimension, vector spaces, row space and row rank of matrix, row echelon matrix, coordinate vectors

What you'll learn
How to get Row Echelon matrix , Column echelon Matrix, Elementray matrices, Row Space and Row Rank of matrix, Column Space and Column rank of Matrix.
How to find the Basis and Dimension of Row Space or Column Space of Matrix
How to find the Basis of Vector Space generated by given Polynomials and also by given Matrices.
Coordinate Vector of a vector relative to the Standard Basis.
Requirements
Basic Knowledge of Vector Spaces and Subspaces.
Description
Introducing this 5 hour 23 minute Course on
ROW SPACE AND ROW RANK OF MATRIX
The Course includes_
The concepts of leading entries of rows and column indices.
The definition for
Row Echelon Matrix
and its properties.
The examples of Row Echelon Matrices and definition of Elementary Row Operations and Elementary Column Operations.
Methods of reducing a matrix into row echelon form
To get Column echelon form matrix from given matrix.
Definition of
Row Space and Row rank of matrix
.
Definition of
Column Space and Column Rank of matrix.
Theorems on Row space and row rank of matrix.
Theorems on Column space and column rank of matrix.
The equivalent statements on matrices for row space and column space of matrix
To get
Basis and Dimension
of row space of matrix and
To get Basis and Dimension of column space of matrix.
Basis for the vector space generated by Polynomials.
Basis for the vector space generated by matrices.
Concept of
Coordinate Vectors relative to standard basis and Solved Examples.
And, To get Basis for vector space generated by given polynomials or matrices using Coordinate vectors .
Assignments on Basis and Dimensions including all the Expected theorems and all types of examples based on the above contents.
Thank You
Who this course is for:
Bachelor of science students, Master of mathematical sciences, gradiuate and post graduate students, students of linear algebra, students of vector spaces linear algebra, linear algebra


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