A matrix is an ordered rectangular array of numbers that represents data. There are different types of matrices including row matrices, column matrices, zero matrices, square matrices, diagonal matrices, scalar matrices, and identity matrices. Matrices can be added or subtracted if they are the same size by adding or subtracting the corresponding entries. Matrix multiplication involves multiplying the rows of the first matrix by the columns of the second matrix to produce an output matrix. The transpose of a matrix is formed by interchanging its rows and columns.

1. BASIC CONCEPT OF MATRIX

2. DEFINITION OF MATRIX
 A matrix is an ordered rectangular array of numbers
that representation some data.
 A matrix on its own has no value – it is just a
representation of data.
 Forms the basis of computer programming.

3. TYPES OF MATRIX
 Row matrix : it having only one row. Ex- [ 1 4 5 ]
 Column matrix : it having only one column. Ex-
 Zero matrix : A matrix is called a zero matrix if all the
entries are 0. Ex-
 Square matrix: if number of rows is equal to number of
columns. Ex-
 Diagonal matrix: A square matrix is called diagonal matrix,
if all of its non-diagonal elements are zero.
Ex-
 Scalar matrix: A square matrix is called scalar matrix if
diagonal elements are same and other are “0”.
Ex-

4. TYPES OF MATRIX
 Identity/ unit matrix: A square matrix is identity if
diagonal entries are 1 and other are 0. Ex-
REPRESENTATION OF MATRIX
 A=[aij]M×N
 aij= element in row ‘i’ and column ‘j’ ,where ‘a’ is
an element in the matrix.

5. ADDITION OF TWO MATRICES
 When two matrices of same order are added, their
corresponding entries are added.
 Type equation here.,
 A =
𝟐 𝟒𝟓 𝟕𝟐
𝟔 𝟑 𝟎
𝟕 𝟗 𝟏𝟎
𝟑 × 𝟑 𝐁 =
𝟒𝟎 𝟕 𝟗
𝟔 𝟏 𝟐
𝟕 𝟐 𝟖
3×3
 A+B=
𝟐 𝟒𝟓 𝟕𝟐
𝟔 𝟑 𝟎
𝟕 𝟗 𝟏𝟎
+
𝟒𝟎 𝟕 𝟗
𝟔 𝟏 𝟐
𝟕 𝟐 𝟖
=
(𝟐 + 𝟒𝟎) (𝟒𝟓 + 𝟕) (𝟕𝟐 + 𝟗)
(𝟔 + 𝟔) (𝟑 + 𝟏) (𝟎 + 𝟐)
(𝟕 + 𝟕) (𝟗 + 𝟐) (𝟏𝟎 + 𝟖)
=
𝟒𝟐 𝟓𝟐 𝟖𝟏
𝟏𝟐 𝟒 𝟐
𝟏𝟒 𝟏𝟏 𝟏𝟖
3×3
 Only matrices of the same order can be added.
 Rule 1: A+B=B+A

6. SUBTRACTION OF TWO MATRICES
 When two matrices of same order are subtracted, their
corresponding entries are subtracted.
 A=
𝟏𝟖 𝟐𝟔 𝟏𝟐
𝟏𝟎 𝟏𝟏 𝟏𝟐
𝟖 𝟏𝟎 𝟏𝟔
𝟑 × 𝟑 𝐁 =
𝟕 𝟐 𝟏𝟓
𝟏𝟑 𝟑 𝟓
𝟓 𝟖 𝟗
3×3
 A-B=
𝟏𝟖 𝟐𝟔 𝟏𝟐
𝟏𝟎 𝟏𝟏 𝟏𝟐
𝟖 𝟏𝟎 𝟏𝟔
−
𝟕 𝟐 𝟏𝟓
𝟏𝟑 𝟑 𝟓
𝟓 𝟖 𝟗
=
(𝟏𝟖 − 𝟕) (𝟐𝟔 − 𝟐) (𝟏𝟐 − 𝟏𝟓)
(𝟏𝟎 − 𝟏𝟑) (𝟏𝟏 − 𝟑) (𝟏𝟐 − 𝟓)
(𝟖 − 𝟓) (𝟏𝟎 − 𝟖) (𝟏𝟔 − 𝟗)
=
𝟏𝟏 𝟐𝟒 −𝟑
−𝟑 𝟖 𝟕
𝟑 𝟐 𝟕
 B-A=
𝟕 𝟐 𝟏𝟓
𝟏𝟑 𝟑 𝟓
𝟓 𝟖 𝟗
−
𝟏𝟖 𝟐𝟔 𝟏𝟐
𝟏𝟎 𝟏𝟏 𝟏𝟐
𝟖 𝟏𝟎 𝟏𝟔
=
−𝟏𝟏 −𝟐𝟒 𝟑
𝟑 −𝟖 −𝟕
−𝟑 −𝟐 −𝟕
𝟑 × 𝟑
 Role 2: A-B ≠ B-A

7. MULTIPLICATION OF MATRICES
 In matrix multiplication, the production of m×n matrix. for,
example, matrix A is a 2×3 matrix and matrix B is a 3×4
matrix, then AB is a 2×4 matrices.
 A=
𝟎 𝟐
𝟐 𝟏
𝟑
𝟒
𝟐 × 𝟑 𝐁=
𝟏 𝟓 𝟖
𝟐 𝟔 𝟑
𝟏 𝟐𝟐 𝟏𝟏
𝟗
𝟏𝟎
𝟕
3× 𝟒
 AB= (𝟎 × 𝟏 + 𝟐 × 𝟐 + 𝟑 × 𝟏) (𝟎 × 𝟓 + 𝟐 × 𝟔 + 𝟑 × 𝟐𝟐)
(𝟐 × 𝟏 + 𝟏 × 𝟐 + 𝟒 × 𝟏) (𝟐 × 𝟓 + 𝟏 × 𝟔 + 𝟒 × 𝟐𝟐)
(𝟎 × 𝟖 + 𝟐 × 𝟑 + 𝟑 × 𝟏𝟏)
(𝟐 × 𝟖 + 𝟏 × 𝟑 + 𝟒 × 𝟏𝟏)
(𝟎 × 𝟗 + 𝟐 × 𝟏𝟎 + 𝟑 × 𝟕)
(𝟐 × 𝟗 + 𝟏 × 𝟏𝟎 + 𝟒 × 𝟕)
=
𝟕 𝟕𝟖
𝟖 𝟏𝟎𝟒
𝟑𝟗
𝟔𝟑
𝟒𝟏
𝟓𝟔
2× 𝟒

8. TRANSPOSE OF MATRIX
 Matrix formed by interchanging rows and columns of A
is called A transpose(A’).

9. THANKING YOU