Business Maths and
Linear Algebra
Introduction to Linear Transformations
Lecture # 10
Business Maths and Linear Algebra
Instructor:Hameed Khan
2
Business Maths and Linear Algebra
Instructor:Hameed Khan
3
Applications of Linear Systems
Business Maths and L
Business Maths and
Linear Algebra
The Matrix Equations Ax=b
Lecture # 6
The Matrix Equations Ax = b
Business Maths and Linear Algebra
Instructor:Hameed Khan
2
Business Maths and Linear Algebra
Instructor:Hameed Khan
3
Business Maths and Linear Algebra
Ins
Business Maths and
Linear Algebra
Row Reduction and Echelon Forms
Lecture # 3
Business Maths and Linear Algebra
Instructor:Hameed Khan
2
The solution is unique.
Business Maths and Linear Algebra
Instructor:Hameed Khan
3
Business Maths and Linear Algebra
I
Business Maths and
Linear Algebra
Eigenvectors and Eigenvalues,
The Characteristic Equation
Lecture # 14
Eigen Vectors and Eigenvalues
Business Maths and Linear Algebra
Instructor:Hameed Khan
2
Business Maths and Linear Algebra
Instructor:Hameed Khan
3
Bu
Business Maths and
Linear Algebra
Solution Sets of Linear Systems
Lecture # 7
Solution Sets of Linear Systems
Business Maths and Linear Algebra
Instructor:Hameed Khan
2
Business Maths and Linear Algebra
Instructor:Hameed Khan
3
Business Maths and Linear A
Business Maths and
Linear Algebra
Row Reduction and Echelon Forms
Lecture # 4
The Row Reduction Algorithm
Business Maths and Linear Algebra
Instructor:Hameed Khan
2
Business Maths and Linear Algebra
Instructor:Hameed Khan
3
Business Maths and Linear Algeb
Business Maths and
Linear Algebra
Eigenvectors and Eigenvalues,
The Characteristic Equation
Lecture # 15
The Characteristic Equation
Business Maths and Linear Algebra
Instructor:Hameed Khan
2
Business Maths and Linear Algebra
Instructor:Hameed Khan
3
Busi
Business Maths and
Linear Algebra
Diagonalization
Lecture # 16
Diagonalization
Business Maths and Linear Algebra
Instructor:Hameed Khan
2
Business Maths and Linear Algebra
Instructor:Hameed Khan
3
Business Maths and Linear Algebra
Instructor:Hameed Khan
4
Business Maths and
Linear Algebra
The Inverse of a Matrix
Lecture # 11
The Inverse of a Matrix
Business Maths and Linear Algebra
Instructor:Hameed Khan
2
Business Maths and Linear Algebra
Instructor:Hameed Khan
3
Definition:
Business Maths and Linear Alge
Business Maths and
Linear Algebra
Introduction to Linear Transformations
Lecture # 9
Introduction to Linear Transformations
Business Maths and Linear Algebra
Instructor:Hameed Khan
2
Business Maths and Linear Algebra
Instructor:Hameed Khan
3
Business Math
Business Math and Linear Algebra
Iman Sohail
ERP: 08491
Applications of linear programming in business and economics:
1. Production Management:
Linear programming is applied for determining the optimal allocation of such resources
as materials, machines,
Business Maths and
Linear Algebra
Properties of Determinants
Lecture # 13
3.1 Introduction to Determinants
Business Maths and Linear Algebra
Instructor:Hameed Khan
2
Theorem 1:
Business Maths and Linear Algebra
Instructor:Hameed Khan
3
Business Maths and
Business Maths and
Linear Algebra
Characterizations of Invertible Matrices
Lecture # 12
2.3 Characterizations of Invertible Matrices
Business Maths and Linear Algebra
Instructor:Hameed Khan
2
Theorem 8:
Business Maths and Linear Algebra
Instructor:Hameed