# Chapter 03: Matrices and Determinants

Notes (Solutions) of Chapter 03: Matrices and Determinants, Text Book of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Text Book Board, Lahore.

• Introduction
• Addition of Matrices
• Scalar Multiplication
• Subtraction of Matrices
• Multiplication of two Matrices
• Determinant of a $2\times2$ matrix
• Singular and nonsingular Matrices
• Adjjoint of a $2\times2$ matrix
• Inverse of $2\times2$ matrix
• Solution of simultaneous linear equations by using matrices
• Exercise 3.1
• Field
• Properties of Matrix Addition, Scalar Multiplication and Matrix Multiplicaton.
• Exercise 3.2
• Determinants
• Minor and Cofactor f an Element of a Maatrix or its Determinant
• Determinant of a Square Matrix of Order $n\geq 3$
• Properties of Determinants with help in their Evaluation
• Adjoint and Inverse of a Square Matrix of order $n\geq 3$
• Exercise 3.3
• Elementary Row and Column Operations on a Matrix
• Echelon and Reduce Echelon form of Martices
• Exercise 3.4
• System of Linear Equation
• Homogeneous Linear Equation
• Non-Homogeneous Linear Equations
• Cramer`s Rule
• Exercise 3.5

The following notes are send by Muhammad Fiaz Hussain. We are very thankful to him for sending these notes.

The following short questions was send by Mr. Akhtar Abbas.

• fsc/fsc_part_1_solutions/ch03