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Introduction to Book

Chapter 01: Matrices

1.1: Introduction to Matrices

1.1.2: Rows and Columns of Matrix

1.1.3: Order (or dimension) of a Matrix

1.1.4: Equality of two Matrices

Exercise 1.1 -> Question 01

Exercise 1.1 -> Question 02

Exercise 1.1 -> Question 03

Exercise 1.1 -> Question 04

Exercise 1.1 -> Question 05

Exercise 1.1 -> Question 06

Exercise 1.1 -> Question 07

1.2: Types of Matrices

Exercise 1.2 -> Question 01

Exercise 1.2 -> Question 02

Exercise 1.2 -> Question 03

Exercise 1.2 -> Question 04

1.3: Addition & Subtraction of matrices

1.3.3: Multiplication of a matrix by a real number

1.3.4(a): Commutative law under addition

1.3.4(b): Associative law for matrix addition

1.3.5: Additive identity of matrices

1.3.6: Additive inverse of a matrix

Exercise 1.3 -> Question 01

Exercise 1.3 -> Question 02

Exercise 1.3 -> Question 03

Exercise 1.3 -> Question 04

Exercise 1.3 -> Question 05

Exercise 1.3 -> Question 06

Exercise 1.3 -> Question 07

Exercise 1.3 -> Question 08

Exercise 1.3 -> Question 09

Exercise 1.3 -> Question 10

Exercise 1.3 -> Question 11

Exercise 1.3 -> Question 12

Exercise 1.3 -> Question 13

Exercise 1.3 -> Question 14

1.4.1: Conformability for multiplication of matrices

1.4.2: Commutative law of multiplication of matrices

1.4.3: Associative law under multiplication

1.4.4: Distributive laws of multiplication over addition

1.4.5: Multiplicative identity of a matrix

1.4.6: Transpose of a matrix

1.4.7: Verification of the transpose

Exercise 1.4 -> Question 01

Exercise 1.4 -> Question 02

Exercise 1.4 -> Question 03

Exercise 1.4 -> Question 04

Exercise 1.4 -> Question 05

Exercise 1.4 -> Question 06

Exercise 1.4 -> Question 07

Exercise 1.4 -> Question 08

Exercise 1.4 -> Question 09

Exercise 1.4 -> Question 10

Exercise 1.4 -> Question 11

Exercise 1.4 -> Question 12

1.5.1: Determinant of a square matrix

1.5.2: Singular and Non Singular matrices

1.5.3: Adjoint of a matrix

1.5.4: Multiplicative inverse of a matrix

1.5.5: use of adjoint method to calculate inverse of a non singular matrix

1.5.6: Verification of the result AA^-1

1.5.7: Verification of the result (AB)^-1

Exercise 1.5 -> Question 01

Exercise 1.5 -> Question 02

Exercise 1.5 -> Question 03

Exercise 1.5 -> Question 04

Exercise 1.5 -> Question 05

Exercise 1.5 -> Question 06

1.6: Solution of simutaneous linear equations by Inversion Method with example 24 & 25

1.6.1: Cramer's Rule with example 26

1.6.2: Real life problems leading to simultaneous equations

Exercise 1.6 -> Question 01

Exercise 1.6 -> Question 02

Exercise 1.6 -> Question 03

Exercise 1.6 -> Question 04

Exercise 1.6 -> Question 05

Exercise 1.6 -> Question 06

Review Exercise 1 -> Question 02

Review Exercise 1 -> Question 03

Review Exercise 1 -> Question 04

Review Exercise 1 -> Question 05

Chapter 02: Real and Complex Numbers

2.1: Real numbers with example 1 and 2

Exercise 2.1 -> Questions 01 - 10

Exercise 2.1 -> Question 11

Exercise 2.1 -> Question 12

2.2.1.1: Addition properties of real number system

2.2.1.2: Multiplication properties of real number system

2.2.1.3: Distributive property of multiplication over addition

2.2.1.4: Properties of Equality of real numbers

2.2.2: Properties of Inequality of Real numbers

Example 3 and 4

Exercise 2.2 -> Question 01

Exercise 2.2 -> Question 02

Exercise 2.2 -> Question 03

Exercise 2.2 -> Question 04

2.3.1: Concept of Radicals and Radicands with examples 5 to 9

Example 10 and 11

Exercise 2.3 -> Question 01

Exercise 2.3 -> Question 02

Exercise 2.3 -> Question 03

Exercise 2.3 -> Question 04

2.4: Laws of exponents/ indices

Exercise 2.4 -> Question 01

Exercise 2.4 -> Question 02

Exercise 2.4 -> Question 03

Exercise 2.4 -> Question 04

Exercise 2.4 -> Question 05

2.5: Complex Numbers

2.6: Operations on complex numbers

Operations on complex numbers examples

Exercise 2.5 -> Question 01

Exercise 2.5 -> Question 02

Exercise 2.5 -> Question 03

Exercise 2.5 -> Question 04

Exercise 2.5 -> Question 05

Exercise 2.5 -> Question 06

Review Exercise 2 -> Question 03

Review Exercise 2 -> Question 04

Review Exercise 2 -> Question 05

Review Exercise 2 -> Question 06

Review Exercise 2 -> Question 07

Chapter 03: Logarithm

3.1: Scientific Notation

3.1.2: How to write a number x from its scientific notation to standard form

Exercise 3.1 -> Question 01

Exercise 3.1 -> Question 02

Exercise 3.1 -> Question 03

Exercise 3.2 -> Question 01

Exercise 3.2 -> Question 02

Exercise 3.2 -> Question 03

3.2.1: Defining Common logarithm, Characteristic and Mantisa

Exercise 3.3 -> Question 01

Exercise 3.3 -> Question 02

Exercise 3.3 -> Question 03

3.2.3: Anti-Logrithm

Exercise 3.4 -> Question 01

Exercise 3.4 -> Question 02

3.4: Laws of logarithm

Exercise 3.5 -> Question 01

Exercise 3.5 -> Question 02

Exercise 3.5 -> Question 03

Exercise 3.5 -> Question 04

3.5: Application of Logarithm

Exercise 3.6 -> Question 01

Exercise 3.6 -> Question 02

Review Exercise 3 -> Question 02

Review Exercise 3 -> Question 03

Review Exercise 3 -> Question 04

Review Exercise 3 -> Question 05

Review Exercise 3 -> Question 06

Review Exercise 3 -> Question 07

Review Exercise 3 -> Question 08

Review Exercise 3 -> Question 09

Review Exercise 3 -> Question 10

Chapter 4: Algebraic Expressions and Algebraic Formulas

4.1: Algebraic Expressions

4.1.1: Rational Expressions

4.1.4: Lowest terms of a Rational expression

4.1.7: Finding Sum and Difference of Rational Expressions

4.1.8: Product and Division of a Rational Expression

Exercise 4.1 -> Question 01

Exercise 4.1 -> Question 02

Exercise 4.1 -> Question 03

Exercise 4.1 -> Question 04

Exercise 4.1 -> Question 05

Exercise 4.1 -> Question 06

Exercise 4.1 -> Question 07

4.1.10: Value of an algebraic Expression at some particular real number

Exercise 4.2 -> Question 01

Exercise 4.2 -> Question 02

Exercise 4.2 -> Question 03

Exercise 4.2 -> Question 04

Exercise 4.2 -> Question 05

4.2: Algebraic Formulas

Exercise 4.3 -> Question 01

Exercise 4.3 -> Question 02

Exercise 4.3 -> Question 03

Exercise 4.3 -> Question 04

Exercise 4.3 -> Question 05

Exercise 4.3 -> Question 06

4.2.2: Deriavation of the formula (a+b+c)^2

Exercise 4.4 -> Question 01

Exercise 4.4 -> Question 02

Exercise 4.4 -> Question 03

Exercise 4.4 -> Question 04

Exercise 4.4 -> Question 05

Exercise 4.4 -> Question 06

4.2.3: Deriavation of the formula (a+b)^3 and (a-b)^3

Exercise 4.5 -> Question 01

Exercise 4.5 -> Question 02

Exercise 4.5 -> Question 03

Exercise 4.5 -> Question 04

Exercise 4.5 -> Question 05

Exercise 4.5 -> Question 06

Exercise 4.5 -> Question 07

Exercise 4.5 -> Question 08

Exercise 4.5 -> Question 09

Derivation of the formula a^3 +/- b^3

Exercise 4.6 -> Question 01

Exercise 4.6 -> Question 02

Exercise 4.6 -> Question 03

Exercise 4.6 -> Question 04

Exercise 4.6 -> Question 05

4.3: Surds and their Application

Exercise 4.7 -> Question 01

Exercise 4.7 -> Question 02

Exercise 4.7 -> Question 03

Exercise 4.7 -> Question 04

Exercise 4.7 -> Question 05

Exercise 4.7 -> Question 06

Exercise 4.7 -> Question 07

Exercise 4.7 -> Question 08

Exercise 4.7 -> Question 09

Exercise 4.7 -> Question 10

Review Exercise 4 -> Question 02

Review Exercise 4 -> Question 03

Review Exercise 4 -> Question 04

Review Exercise 4 -> Question 05

Review Exercise 4 -> Question 06

Review Exercise 4 -> Question 07

Review Exercise 4 -> Question 08

Review Exercise 4 -> Question 09

Review Exercise 4 -> Question 10

Chapter 5: Factorization

5.1: Factorization

Exercise 5.1 -> Question 01

Exercise 5.1 -> Question 02

Exercise 5.1 -> Question 03

Exercise 5.1 -> Question 04

Exercise 5.1 -> Question 05

Exercise 5.1 -> Question 06

Exercise 5.1 -> Question 07

Exercise 5.1 -> Question 08

Exercise 5.1 -> Question 09

Exercise 5.1 -> Question 10

5.1.6: Factorization of the Expression of the Type- I

Exercise 5.2 -> Question 01

Exercise 5.2 -> Question 02

Exercise 5.2 -> Question 03

Exercise 5.2 -> Question 04

Exercise 5.2 -> Question 05

Exercise 5.2 -> Question 06

Exercise 5.2 -> Question 07

Exercise 5.2 -> Question 08

Exercise 5.2 -> Question 09

Exercise 5.2 -> Question 10

5.1.7: Factorization of Trinomials of the type- II

Exercise 5.3 -> Question 01

Exercise 5.3 -> Question 02

Exercise 5.3 -> Question 03

Exercise 5.3 -> Question 04

Exercise 5.3 -> Question 05

Exercise 5.3 -> Question 06

Exercise 5.3 -> Question 07

Exercise 5.3 -> Question 08

Exercise 5.3 -> Question 09

Exercise 5.3 -> Question 10

Exercise 5.3 -> Question 11

Exercise 5.3 -> Question 12

Exercise 5.3 -> Question 13

5.1.9: Factorization of the Type- IV

5.1.12: Factorization of the Type- V

Exercise 5.4 -> Question 01

Exercise 5.4 -> Question 02

Exercise 5.4 -> Question 03

Exercise 5.4 -> Question 04

Exercise 5.4 -> Question 05

Exercise 5.4 -> Question 06

Exercise 5.4 -> Question 07

Exercise 5.4 -> Question 08

Exercise 5.4 -> Question 09

Exercise 5.4 -> Question 10

5.1.13: Factorization of an Expression of the Type- VI

Exercise 5.5 -> Question 01

Exercise 5.5 -> Question 02

Exercise 5.5 -> Question 03

Exercise 5.5 -> Question 04

Exercise 5.5 -> Question 05

Exercise 5.5 -> Question 06

Exercise 5.5 -> Question 07

Exercise 5.5 -> Question 08

Exercise 5.5 -> Question 09

Exercise 5.5 -> Question 10

5.2/5.3: Remainder Theorem and Factor Theorem

Exercise 5.6 -> Question 01

Exercise 5.6 -> Question 02

Exercise 5.6 -> Question 03

Exercise 5.6 -> Question 04

Review Exercise 5 -> Question 04

Review Exercise 5 -> Question 05

Review Exercise 5 -> Question 06

Review Exercise 5 -> Question 07

Review Exercise 5 -> Question 08

Review Exercise 5 -> Question 09

Review Exercise 5 -> Question 10

Chapter 6: Algebraic Manipulation

6.1: Highest Common Factor and Least Common Multiple

6.1: Highest Common Factor and Least Common Multiple (Example 10 & 11)

Exercise 6.1 -> Question 01

Exercise 6.1 -> Question 02

Exercise 6.1 -> Question 03

Introduction

In this course, you will learn all the topics in this book without the need of any tutor. If you have still any questions you can ask freely.

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