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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

1.4.5: Multiplicative identity of a matrix

Let we have a matrix I and a matrix A. if these two matrices are so related to each other that IA = AI = A , in other words the multiplication of I with A or A with I doesn't change the value of A then I is called the identity matrix of A.

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