# 3. Matrices

## Matrices

Complete Syllabus of Class 12 Maths Chapter 3 Matrices:

Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Non- commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).

NCERT Exercise 3.1

NCERT Exercise 3.2

NCERT Exercise 3.3

NCERT Exercise 3.4

NCERT Miscellaneous Exercise NCERT Chapter 3 Examples

## Lecture - 1

• Basics of matrix (matirces): row, column, order of matrix
• NCERT Exercise 3.1 (Q1 to Q9)

## Lecture - 2

• Types of matrices: row matrix, column matrix, square matrix, diagonal matrix, scalar matrix, identity matrix, null matrix
• NCERT Exercise 3.1 (Q8 & Q10)
• Addition and Subtraction of Matrices
• NCERT Exercise 3.2 (Q1 to Q5)
• Multiplication of matrix with a scalar
• Multiplication of two matrices

## Lecture - 3

NCERT Exercise 3.2 (Q4 to Q15)

## Lecture - 4

• NCERT Exercise 3.2 (Q16 to Q22)
• Transpose of a matrix, properties of transpose
• NCERT Exercise 3.3 Question 1

## Lecture - 5

• Properties of transpose
• Symmetric matrices and skew symmetric matrices
• Sum of symmetric and skew symmetric matrices
• NCERT Exercise 3.3 (Q2 to Q10)

## Lecture - 6

NCERT Miscellaneous Exercise (Q1 to Q3)

## Lecture - 7

NCERT Miscellaneous Exercise (Q4 to Q12)

## Lecture - 8

• Working with elementary transformations or elementary operations
• Working with identity matrices
• NCERT Exercise 3.4 Question 1

## Lecture - 9

NCERT Exercise 3.4 (Q2 to Q14)

## Lecture - 10

NCERT Exercise 3.4 (Q15 to Q18)