Dear Students,

Today, almost 90% of our students have joined different Academies for learning purpose. Some of them hired tutors and are charging high fee. We realize the factor and are very well aware that it is very much difficult for the parents to afford the high fee of different Academies / Tutors. We also concluded that the Academies are not providing good teaching services to the students but charging high fee from students. After realizing the factors we have uploaded the videos prepared by SABAQ foundation on our website which will really beneficial for the students as well as the people who are serving as teachers of different subjects in different institutions.

From this section you can download / view Video Lectures on Mathematics **Class 11th / F.Sc / ICS Part-I** for free. These Videos for **F.Sc** students have been prepared by SABAK Foundation for the ease of students as per new and updated syllabus/course prescribed by Federal Board of Intermediate & Secondary Education (FBISE), Islamabad – Pakistan and other BISE(s)/Boards of Pakistan. We are fully hopeful that after after watching/viewing these Video Lectures you will score 90% plus marks in your exams as they have been prepared in a very simple, easy, brief and in simple and lucid language to understand. The purpose of sharing these videos is to promote education in Pakistan and to help those students who really want to learn something. These videos are enough for learning purpose, and after watching these video lectures you will come to know that you are no more in need of any kind of tuition or Academy.

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**Please select the desired subject to download / watch the video from the links given below**:

**Chapter 3: Matrices and Determinants (56 videos)**

**3.1: Introduction**

**Introduction to Matrix****More on Introducing Matrix****Order of Matrix****Equal Matrices****Row Matrix and Column Matrix****Square Matrix and Rectangular Matrix****Null Matrix or Zero Matrix****Transpose of a Matrix****Negative of Matrix****Diagonal Matrix****Scalar Matrix****Identity Matrix****Addition of Matrices****Subtraction of Matrices****Multiplication of Matrix by a Real Number****Multiplicative Identity of a Matrix****More on Multiplication of Matrices**

**3.2: Determinant of a 2×2 Matrix**

**Determinant of 2-by-2 Matrix****Singular and Non-singular Matrix****Adjoint of a Matrix****Multiplicative Inverse of a Non-Singular Matrix****Inverse of Matrix using Adjoint**

**3.3: Solution of Simultaneous Linear Equations By Using Matrices**

**3.4: Field**

**3.5: Properties of Matrix Addition, Scalar Multiplication and Matrix Multiplication**

**Commutative Law under Addition for Matrices****Associaitve Law under Addition for Matrices****Additive Identity of a Matrix****Additive Inverse of a Matrix****Multiplication of Matrices****Associative law under Multiplication of matrices****Distributive Law of Multiplication over Addition for Matrices****Commutative Law of Multiplication of Matrices****Prove That c(AB) = (cA)B = A(cB)**

**3.6: Determinants**

**Minor of an Element of a Matrix or Its Determinant****Cofactor of an Element of a Matrix****Determinant of a Sqaure Matrix of Order 3 or greater**

**3.7: Properties of Determinants Which Help in Their Evaluation**

**3.8: Adjoint and Inverse of a Square Matrix of Order n = 3 or n > 3**

**Inverse of Matrix using Adjoint****Adjoint of a Square Matrix of Order n = 3 or n > 3****More on Matrix Inverse Using Adjoint**

**3.9: Elementary Row and Column Operations on a Matrix**

**Deriving a Method For Determining Inverses****Inverse of Matrix by Row Operation****Inverse of Matrix by Column Operation****Triangular Matrices****Symmetric and Skew-Symmetric Matrices****Hermitian and Skew Hermitian Matrix**

**3.10: Echelon and Reduced Echelon Forms of Matrices**

**Echelon and Reduced Echelon Form of Matrix****Echelon Form of Matrix****Reduced Echelon Form of Matrix****Rank of a Matrix**

**3.11: Systems of Linear Equations**

**Solution of System of Linear Equations by Row Operation****Solution of Homogeneous Linear Equations****More on Solution of Homogeneous Linear Equations**