Page 123 - Touhpad Ai

The entries in the rows represent number of oranges and apples bought by Ganga, Hemant and Gargi respectively.
Or in another form as:
 12 10 5 Row 1
 

 5 7 2 Row 2
Col 1 Col 2 Col3
Here, the entries in the columns represent the number of oranges and apples bought by Ganga, Hemant and
Gargi respectively.

We denote matrices by capital letters. For example:
2 7

A 0 5
3 1
3 x 2
Order of Matrix
A matrix having m rows and n columns is called a matrix of order m × n or simply m × n matrix (read as an
m by n matrix). So, referring to the above example, matrix A is a 3 x 2 matrix. The number of elements present in a
matrix is given by m × n ⇒ 3 × 2 = 6 elements.
Each individual element is represented as a where i represents row and j represents column.
ij
24 3 a a a
A 11 12 13
a
75 9 23 21 a 22 a 23
x
th
In general, a , is an element lying in the i row and j column. We can also call it as the (i, j) element of the matrix.
th
th
ij
Types of Matrices
Matrices can be of many types:
u Row Matrix: A matrix having only one row is known as row matrix. For example:
A = [2 4 5]
1 x 3
u Column Matrix: A matrix having only one column is known as column matrix. For example:
3

A 1

2
31
u Square Matrix: A matrix having equal number of rows and columns is known as square matrix. For example:
3 4 – 5
Since m = n
A 1 7 2
8 – 3 11 Order ⇒ m x m
x
33
u Diagonal Matrix: A matrix with all the elements zero except its leading diagonal is known as a diagonal matrix.
For example:
20 0 

A = 0 7 0   Also called Primary Diagonal

 0 0  6
  3 x 3

Mathematics for AI 121