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

 

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  • Q1

    A matrix in which all non diagonal elements are zero is known as

    Marks:1
    Answer:

    diagonal matrix.

    Explanation:
    A square matrix B = [bij]m×n is said to be a diagonal matrix, if all its non diagonal elements are zero, that is a matrix B = [bij]m×n is said to be a diagonal matrix, if bij = 0, when i ¹ j.
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  • Q2

    A matrix, in which the number of rows is equal to the number of columns, is known as

    Marks:1
    Answer:

    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’.

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  • Q3

    A matrix having only one row is known as

    Marks:1
    Answer:

    row matrix.

    Explanation:

    A matrix is said to be a row matrix, if it has only one row.

    In general, A = [aij]n is a column matrix of order 1 n.

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  • Q4

    A matrix having only one column is known as

    Marks:1
    Answer:

    column matrix.

    Explanation:

    A matrix is said to be a column matrix, if it has only one column.

    In genral, A = [aij]m×1 is a column matrix of order m 1.

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  • Q5

    If a matrix has m rows and n columns, then the order of the matrix is

    Marks:1
    Answer:

    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).
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