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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
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 × 2 matrix. The number of
elements present in a matrix is given by m x n => 3 x 2 = 6 elements.
Each individual element is represented as a where i represents row and j represents column.
ij
2 4 3
A = a11 a12 a13
7 5 9 a23
a21 a22
th
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
ij
Types of Matrices
Matrices can be of many types:
• Row Matrix: Matrices having only one row are known as row matrix.
A = 2 45 13
×
• Column Matrix: Matrices having only one column are known as column matrix.
3
A = − 1
2
31
×
• Square Matrix: Matrices having equal number of rows and columns are known as square matrix.
3 4 --5 3 =
A = 1 A = − 2 1 Since m n
7
Order⇒×
m m
8--3 11 2
33×
x
33
• Diagonal Matrix: A matrix with all the elements zero except its leading diagonal is known as a diagonal
matrix.
20 0
A = 070 Also called Primary Diagonal
006
• Scalar Matrix: A matrix in which all the diagonal elements are equal and all other elements are zero is
known as a scalar matrix.
Maths for AI 161

