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Matrices, Order of a Matrix, Row and Column Matrix is considered one of the most asked concept.
7 Questions around this concept.
The number of 3 x 3 non-singular matrices, with four entries as 1 and all other entries as 0, is
A rectangular arrangement of objects (numbers or symbols or any other objects) is called a matrix (plural: matrices).
Example:
Order of Matrix
Rows and Columns:
The horizontal objects denote a row and vertical ones denote a column.
Eg, in first matrix above, elements 2, 4 and -3 lie in first row and 5, 4 and 6 in second row
Also 2, 5, lie in first column, 4,4 in second column, and -3, 6 in third column
Order of a matrix:
Matrix of order m × n, (read as m by n matrix) means that the matrix has m number of rows and n number of columns.
E.g.,
Representation of a m x n matrix:
This representation can be represented in a more compact form as
Where represents element of ith row and jth column and i = 1,2,...,m; j = 1,2,...,n.
For example, to locate the entry in matrix A identified as aij, we look for the entry in row i, column j. In matrix A, shown below, the entry in row 2, column 3 is a23.
Note:
Matrix is only a representation of the symbol, number or object. It does not have any value. Usually, a matrix is denoted by capital letters.
Types of Matrices
Row matrix: A matrix containing only one row is called a row matrix. So a matrix is said to be a row matrix when m = 1.
It can be denoted by
Eg,
[ 1 32 81 -32 ] has only 1 row. It has order 1 x 4
Column matrix: A matrix containing only one column is known as a column matrix. So a matrix is said to be column matrix when n = 1.
It is denoted by
Eg,
This matrix has order 4 x 1
Note:
A matrix that contains only one row or one column is also known as a vector i.e. row vectors and column vectors.
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