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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