Matrices and Their Types
• A matrix is an ordered rectangular array of numbers or functions arranged in rows and columns. A matrix having m rows and n columns is called a matrix of order m x n. In general, an m × n matrix is represented as below:
• Two matrices are comparable matrices iff each one of them contains as many rows and columns as the other.
• Two matrices are said to be equal if they are of the same order and each element of matrix A is equal to the corresponding element of matrix B.
• A matrix is said to be a column matrix if it has only one column.
• A matrix is said to be a row matrix if it has only one row.
• A matrix in which the number of rows is equal to the number of columns, is said to be a square matrix.
• A square matrix is said to be a diagonal matrix if all its non diagonal elements are zero.
• A diagonal matrix is said to be a scalar matrix if all its diagonal elements are equal.
• The diagonal matrix in which each diagonal element is equal to unity is called an identity matrix.
• A matrix is said to be zero matrix or null matrix if all its elements are zero.
• A square matrix is said to be an upper triangular matrix iff all the elements below the principal diagonal are zero.
• A square matrix is said to be a lower triangular matrix iff all the elements above the principal diagonal are zero.
• A triangular matrix is said to be strictly triangular matrix if and only if all the elements of the principal diagonal are zero.
Keywords: Matrix, Types of Matrices, Identity Matrix, Equal Matrices, Scalar Matrix, Diagonal Matrix, Order of a Matrix, Comparable Matrices, Column Matrix, Row Matrix, Square Matrix, Zero Matrix
To Access the full content, Please Purchase

Q1
A matrix in which all non diagonal elements are zero is known as
Marks:1Answer:
diagonal matrix.
Explanation:
A square matrix B = [b_{ij}]_{m}_{×n} is said to be a diagonal matrix, if all its non diagonal elements are zero, that is a matrix B = [b_{ij}]_{m}_{×n} is said to be a diagonal matrix, if b_{ij} = 0, when i ¹ j. 
Q2
A matrix, in which the number of rows is equal to the number of columns, is known as
Marks:1Answer:
square matrix.
Explanation:
A matrix is said to be a square matrix, if it has the number of rows equal to the number of columns.
An m n matrix is said to be a square matrix, if m = n and is known as a square matrix of order ‘n’.

Q3
A matrix having only one row is known as
Marks:1Answer:
row matrix.
Explanation:
A matrix is said to be a row matrix, if it has only one row.
In general, A = [a_{ij}]_{1×n} is a column matrix of order 1 n.

Q4
A matrix having only one column is known as
Marks:1Answer:
column matrix.
Explanation:
A matrix is said to be a column matrix, if it has only one column.
In genral, A = [a_{ij}]_{m}_{×1} is a column matrix of order m 1.

Q5
If a matrix has m rows and n columns, then the order of the matrix is
Marks:1Answer:
m n.
Explanation:
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).