Matrix multiplication involves multiplying matrices according to certain rules. A matrix is a rectangular layout of numbers arranged in rows and columns. To multiply matrices, each element in a row of the first matrix is multiplied by the corresponding element in a column of the second matrix and those products are summed to form the element of the product matrix in that row and column. Matrix multiplication is useful in many fields including business, data analysis, geology, and robotics.

1. WELCOME

2. MATRIX
MULTIPLICATION

3. OBJECTIVE :
 What is Matrix ?
What is Matrix Multiplication ?
 How To Calculate ?
Usese of matrix multiplication .

4.  In mathematics, a matrix is a rectangular layout of numbers, symbols
or expressions arranged in rows and columns .
 Example: A =
2 −1 3
9 5 1
3 4 6
, B=
3 −9
5 4

5. WHAT IS MATRIX
MULTIPLICATION ?
A =
1 2 3
4 5 6
B =
1 4
2 5
3 6
M = A.B

6.  Multiplication of a matrix by a scalar
 Multiplication of a matrix by another matrix

7.  MULTIPLICATION OF A MATRIX BY A SCALAR :
A =
2 −1 3
9 5 1
3 4 6
and k = 6
Then , A*k = 5
𝟐 −𝟏 𝟑
𝟗 𝟓 𝟏
𝟑 𝟒 𝟔
=
10 −5 15
45 25 5
15 20 30

8.  MULTIPLICATION OF A MATRIX BY ANOTHER MATRIX :
A =
𝟏 𝟐 𝟑
𝟒 𝟓 𝟔
B =
𝟏 𝟒
𝟐 𝟓
𝟑 𝟔
Then , AB =
𝟏 𝟐 𝟑
𝟒 𝟓 𝟔
*
𝟏 𝟒
𝟐 𝟓
𝟑 𝟔
=
𝟏𝟒 𝟑𝟐
𝟑𝟐 𝟕𝟕

9. 𝟔 𝟏 𝟑
𝟑 𝟓 𝟎
𝟑 𝟑
𝟏 𝟐
𝟓 𝟕
A = 2x3 B=3x2
R1 X C1 R2 X C2
C1 == R2
The Result is : R1 x C2
ROW
S
COLUMN
S

10. EXAMPLE :
A =
𝟔 𝟏 𝟑
𝟑 𝟓 𝟎
B =
𝟑 𝟑
𝟏 𝟐
𝟓 𝟕
AB=
𝟔 𝟏 𝟑
𝟑 𝟓 𝟎
X
𝟑 𝟑
𝟏 𝟐
𝟓 𝟕
=
𝟏𝟖 + 𝟏 + 𝟏𝟓 𝟗 + 𝟓 + 𝟎
𝟏𝟖 + 𝟐 + 𝟐𝟏 𝟗 + 𝟏𝟎 + 𝟎
=
𝟑𝟒 𝟏𝟒
𝟒𝟏 𝟏𝟗
[Ans]

11. If the given data is A =
𝟏 𝟐 𝟑
𝟒 𝟓 𝟔
and B =
𝟎 𝟐 𝟒
𝟔 𝟓 𝟑
𝟖 𝟗 𝟖
𝟏 𝟒
𝟐 𝟓
𝟑 𝟔
Then This Matrix Cannot Exist in Matrix Multiplication .

12. USESSE OF MATRIX
MULTIPLICATION .
 Business and Economy
 Data and Statistics
 Geology
 Robotics and Computer Programming