# 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.

### Contents & summary

- 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

### Solutions

- Exercise 3.1 | View Online | Download PDF (322KB)

- Exercise 3.2 | View Online | Download PDF (507KB)

- Exercise 3.3 (Handwritten) | View Online | Download PDF (493KB)

- Exercise 3.4 (Handwritten) | View Online | Download PDF (560KB)

- Exercise 3.5 | View Online | Download PDF (359KB)

- Exercise 3.5 by Prof. Tahir Nazir | View Online | Download PDF (208KB)

- Exercise 3.5 by Prof. Shariq Mahataab | View Online | Download PDF (262KB)

### Notes by M. Fiaz Hussain

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

- Important Questions | Download PDF

- Exercise 3.3 by Fiaz Hussain | View Online | Download PDF

- Exercise 3.4 by Fiaz Hussain | View Online | Download PDF

### Short Questions

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

- Chapter 03 | View Online | Download PDF