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Determine The Order Of Matrix - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

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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.

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The number of 3 x 3 non-singular matrices, with four entries as 1 and all other entries as 0, is

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Matrices, Order of a Matrix, Row and Column Matrix

A rectangular arrangement of objects (numbers or symbols or any other objects) is called a matrix (plural: matrices).

Example:

  1.         \begin{bmatrix} 2 & 4 & -3\\ 5 & 4 & 6 \end{bmatrix}
  2.         \begin{bmatrix} 2 & 4i + 3 \\ 5 & 4 \\3i & -75 \end{bmatrix}
  3.         \begin{bmatrix} 2\\ -5 \\3i\\71 \end{bmatrix}

 

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.,

  • First matrix has order 2 x 3
  • Second matrix has order 3 x 2
  • Third matrix has order 4 x 1

 

Representation of a m x n matrix:

\begin{bmatrix} a_{11} &a_{12} &... & a_{1n}\\ a_{21}&a_{22} &... &a_{2n} \\ ...& ...& ... & ...\\ a_{m1}&a_{m2} &... &a_{mn} \end{bmatrix}

This representation can be represented in a more compact form as  \left [ a_{ij} \right ]_{m\times n}

Where a_{ij} 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.

A=\left[\begin{array}{lll}{a_{11}} & {a_{12}} & {a_{13}} \\ {a_{21}} & {a_{22}} & {a_{23}} \\ {a_{31}} & {a_{32}} & {a_{33}}\end{array}\right]

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 \mathrm{A=[a_{ij}]_{m\times n}\;}  is said to be a row matrix when m = 1.

It can be denoted by

\\\mathrm{\begin{bmatrix} a_{11} &a_{12} &a_{13} &... &... &a_{1n} \end{bmatrix}_{1\times n}} 

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  \mathrm{A=[a_{ij}]_{m\times n}\;}  is said to be column matrix when n = 1.

It is denoted by

\\\mathrm{\begin{bmatrix} a_{11}\\ a_{21}\\ a_{31}\\ ...\\ ...\\ a_{m1}\end{bmatrix}_{m\times 1}}

Eg,

\begin{bmatrix} 2\\ 32 \\3\\7 \end{bmatrix}

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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Matrices, Order of a Matrix, Row and Column Matrix

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