Page 306 - AI Ver 3.0 Class 11
P. 306
Brainy Fact
We all know that computer understands data only in the form of binary/hexadecimal
numbers. Then, how are images processed by computers?
Consider, the given image: 1 5 0 3 0 0 3 3 0
On the computer/mobile, the image is represented as a 3 2 0 6 2 4 0 3 6 1 4 0 1 2
combination of pixels. This is represented mathematically as 2 4 1 1 5 0 3 3 2 3 0 1
3 0 2 4 2 1
matrices! 2 6 1 0 6 0 3 6
2 4 2 4 4 1 6 1
2 6 1 0 6
2 4
Operations on Matrices
Addition of Matrices
The sum of two matrices is a matrix obtained by adding the corresponding elements of the given matrices. Also, the
two matrices have to be of the same order. For example:
2 4 1 0
A = 6 8 B = − 2 7
7 5 4
32 3 32
×
×
21 4 0 + 3 4
+
A B = 6+− 8 7 ⇒ 4 15
+
+
( ) 2
10 9
+
+
7 3 54
Difference of Matrices
If A and B are two matrices of the same order, then the difference A – B is defined as a matrix where each element is
obtained by subtracting the corresponding elements (a – b ). For example:
ij
ij
12 3 3 2 3−
A = B =
230 23 − 1 0 − 2 23
×
×
13 2 −− 3 3 2 40−
−
−
( ) 2
AB −= ⇒
( ) 2
2 ( 1) 3 0
− − − 0 − − 3 32 23
×
Transpose of a Matrix
T
A matrix obtained by interchanging the rows and columns of a matrix. Transpose of a matrix A is denoted by A’ or A .
If order of matrix A is m × n, then order of transpose of matrix A, i.e., A’ is n x m. For example:
14
12 3
‘
A = A OR A = 24
T
45 6 ×23 36
×32
Multiplication of a Matrix by a Scalar
A scalar is any number. So, if A is a matrix and k is a scalar, then kA is another matrix which is obtained by multiplying
each element of A by the scalar k.
304 Touchpad Artificial Intelligence (Ver. 3.0)-XI

