S. Y. B. Sc.

Linear Algebra II

Course Code: USMT402

Credits: 2 || Lecture/week: 3
Probable/Actual Hrs Available: 4

Unit i : linear transformation

NAME OF UNIT	Titles / Details	Video Lectures	Lecture Notes	Assignments / Practicals	Ratings
Linear Transformation	Defination of Linear Transformation	Lecture 1	Lecture 1	Practical 1	0/5
		Lecture 2	Lecture 2	Practical 2	0/5
		Lecture 3	Lecture 3	Practical 3	0/5
		Lecture 4	Lecture 4	Practical 4	0/5
		Lecture 5	Lecture 5	Practical 5	0/5
		Lecture 6	Lecture 6	Practical 6	0/5
		Lecture 7	Lecture 7	Practical 7	0/5 0/5
		Lecture 8	Lecture 8	Practical 8	0/5
		Lecture 9	Lecture 9		0/5
		Lecture 10	Lecture 10		0/5
		Lecture 11	Lecture 11		0/5
		Lecture 12	Lecture 12		0/5
		Lecture 13	Lecture 13		0/5
		Lecture 14	Lecture 14		0/5
		Lecture 15	Lecture 15		0/5

Linear Algebra I

Course Code: USMT302

Credits: 2 || Lecture/week: 3
Probable/Actual Hrs Available: 45

Unit I : System of Equations and Matrices

NAME OF UNIT	Titles / Details	Video Lectures	Lecture Notes	Assignments / Practicals	Ratings
System of Equations and Matrices	Systems of homogeneous and non-homogeneous linear equations,	Lecture 1	Lecture 1	Practical 1	0/5
System of Equations and Matrices	Simple examples of finding solutions of such systems	Lecture 2	Lecture 2	Practical 2	0/5
System of Equations and Matrices	Geometric and algebraicunderstanding of the solutions. Matrices (with real entries),	Lecture 3	Lecture 3	Practical 3	0/5
System of Equations and Matrices	Matrix representation of system of homogeneous System	Lecture 4	Lecture 4	Practical 4	0/5
System of Equations and Matrices	Matrix representation of system of non-homogeneous System	Lecture 5	Lecture 5	Unit Test I	0/5
System of Equations and Matrices	Algebra of solutions of systems of homogeneous linear equations	Lecture 6	Lecture 6		0/5
System of Equations and Matrices	A system of homogeneous linear equations with number of unknowns more than the number of equations has infinitely many solutions.	Lecture 7	Lecture 7		0/5 0/5
System of Equations and Matrices	Elementary row and column operations.	Lecture 8	Lecture 8		0/5
System of Equations and Matrices	Row equivalent matrices. Row reduction (of a matrix to its row echelon form).	Lecture 9	Lecture 9		0/5
System of Equations and Matrices	Gaussian elimination. Applications to solving systems of linear equations. Examples.	Lecture 10	Lecture 10		0/5
System of Equations and Matrices	Elementary matrices. Relation of elementary row operations with elementary matrices.	Lecture 11	Lecture 11		0/5
System of Equations and Matrices	Invertibility of elementary matrices.	Lecture 12	Lecture 12		0/5
System of Equations and Matrices	Consequences such as (i) a square matrix is invertible if and only if its row echelon form is invertible	Lecture 13	Lecture 13		0/5
System of Equations and Matrices	(ii) invertible matrices are products of elementary matrices.	Lecture 14	Lecture 14		0/5
System of Equations and Matrices	Examples of the computation of the inverse of a matrix using Gauss elimination method	Lecture 15	Lecture 15		0/5

Unit II : Vector Spaces over IR

NAME OF UNIT	Titles / Details	Video Lectures	Lecture Notes	Assignments / Practicals	Ratings
Vector Spaces over IR	Defination of Vector Space Over R	Lecture 1	Lecture 1	Practical 1	0/5
Vector Spaces over IR	Span, Basess, Column Space & Null Space	Lecture 2	Lecture 2	Practical 2	0/5
Vector Spaces over IR		Lecture 3	Lecture 3	Practical 3	0/5
Vector Spaces over IR		Lecture 4	Lecture 4	MCQ's	0/5
Vector Spaces over IR		Lecture 5	Lecture 5		0/5
Vector Spaces over IR		Lecture 6	Lecture 6		0/5
Vector Spaces over IR		Lecture 7	Lecture 7		0/5 0/5
Vector Spaces over IR		Lecture 8	Lecture 8		0/5
Vector Spaces over IR		Lecture 9	Lecture 9		0/5
Vector Spaces over IR		Lecture 10	Lecture 10		0/5
Vector Spaces over IR		Lecture 11	Lecture 11		0/5
Vector Spaces over IR		Lecture 12	Lecture 12		0/5
Vector Spaces over IR		Lecture 13	Lecture 13		0/5
Vector Spaces over IR		Lecture 14	Lecture 14		0/5
Vector Spaces over IR		Lecture 15	Lecture 15		0/5