Position of an Element in a Matrix

A matrix is the rectangular array of m x n numbers in the form of rows and columns. Those numbers are enclosed by [] or (). The order of the matrix m and n is written in the form m x n which means m no of rows, n no of columns. The numbers in the matrix are called the elements of the matrix. We can learn about the position of an element in a matrix on this page along with solved questions.

What are Elements in Matrix?

Entries in a matrix are called the elements of the matrix. The address or position of one element in the matrices is given by listing the rows number and column number. While learning the element position in a matrix, you also have to learn the order of matrices which defines the number of rows, elements in a matrix.

The order of a two-dimensional matrix is the number of rows followed by the number of columns. If a matrix has ‘m’ number of rows and ‘n’ number of columns, then its size or order is m x n and it is read as m by n.

Consider a matrix \( A =\left[
\begin{matrix}
10 & 4 & 6\cr
5 & 1 & 3 \cr
2 & 7 & 8 \cr
\end{matrix}
\right]
\)

The order of the above matrix A is 3 x 3 as it has 3 rows and 3 columns.

The elements of A are 10, 4, 6, 5, 1, 3, 2, 7, and 3.

Step by Step Process to Find Position of Elements in a Matrix

The following are the steps to get the position of an element in a matrix. Go through these simple steps and find the address easily.

  • Take any matrix of any order to get the position of elements.
  • Know the column number and row number of a particular element by counting it.
  • The position of an element is the row number of the element followed by the column number.
  • The way to represent the position of an element in matrices are (row number, column number) or Matrix_Nameij.

Example on Position of an Element in a Matrix

Let us consider a matrix \( Z =\left[
\begin{matrix}
1 & 3 & 7\cr
2 & 8 & 15 \cr
11 & 21 & 26 \cr
\end{matrix}
\right]
\)

The elements in the first row are 1, 3, 7, the second row is 2, 8, 15 and the third row are 11, 21, 26.

The position of 15 is this element falls on 2nd row and 3rd column.

So, 15 is (2, 3)th element of Z.

Problems on Address of Elements in Matrices

Problem 1:
Find the position of element 12 in \( X =\left[
\begin{matrix}
8 & 17 \cr
4 & 12 \cr
5 & 13 \cr
\end{matrix}
\right]
\)

Solution:
Given matrix is \( X =\left[
\begin{matrix}
8 & 17 \cr
4 & 12 \cr
5 & 13 \cr
\end{matrix}
\right]
\)
The element 12 falls on 2nd row, 2nd column.
So, the 12 is (2,2)th element of X.

Problem 2:
Find the position of elements 2, 1, 18 in \( Y =\left[
\begin{matrix}
16 & 18 \cr
14 & 7 \cr
4 & 2 \cr
1 & 3 \cr
\end{matrix}
\right]
\)

Solution:
Given matrix is \( Y =\left[
\begin{matrix}
16 & 18 \cr
14 & 7 \cr
4 & 2 \cr
1 & 3 \cr
\end{matrix}
\right]
\)
Element 2 falls on the 3rd row, 2nd column. So, 2 is (2, 3)th element of Y.
Element 1 falls on 4th row, 1st column. So, 1 is (4, 1)th element
Element 18 falls on 1st row, 2nd column. So, 18 is (1, 2)th element.

Problem 3:
Find the position of all elements in the matrix \( A =\left[
\begin{matrix}
1 & 10 & 20 \cr
3 & 13 & 17 \cr
7 & 21 & 28 \cr
\end{matrix}
\right]
\)

Solution:
Given matrix is \( A =\left[
\begin{matrix}
1 & 10 & 20 \cr
3 & 13 & 17 \cr
7 & 21 & 28 \cr
\end{matrix}
\right]
\)
Here, element 1 falls on row number 1 and column 1.
We say, 1 is the (1, 1)th element. Similarly,
(1, 2)th element = 10
(1, 3)th element = 20
(2, 1)th element = 3
(2, 2)th element = 13
(2, 3)th element = 17
(3, 1)th element = 7
(3, 2)th element = 21
(3, 3)th element = 28

Frequently Asked Question’s

1. How to determine the position o an element in a matrix?

The position of an element in the matrix is determined by checking the row number, column number where it falls. The row number, column number is the exact address of the element.

2. What is the order of the matrix?

The order of a matrix is the size of the matrix. It is the number of rows x number of columns in it.

3. What are elements in the matrix?

Every number in a matrix are called the element of a matrix. The number of elements in the matrix is found by multiplying the number of rows by the number of columns.

4. What is element A23 in the matrix?

A23 is nothing the element or number or entry which is present at 2nd row and 3rd column of the matrix A.

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