Q. 14.2( 21 Votes )

If a matrix has 2

Answer :

We know that in mathematics, a matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

The number of rows and columns that a matrix has is called its order or its dimension. By convention, rows are listed first; and columns second.


We are given with a matrix that has 28 elements.


We know that,


If a matrix has mn elements, then the order of the matrix can be given by m × n, where m and n are natural numbers.


Therefore, for a matrix having 28 elements, that is, mn = 28, possible orders can be found out as follows:


mn = 28


Take m and n to be any number, such that, when it is multiplied it gives 28.


So, let m = 1 and n = 28.


Then, m × n = 1 × 28 (=28)


1 × 28 is a possible order of the matrix having 28 elements.


Take m = 2 and n = 14.


Then, m × n = 2 × 14 (=28)


2 × 14 is a possible order of the matrix having 28 elements.


Take m = 4 and n = 7.


Then, m × n = 4 × 7 (=28)


4 × 7 is a possible order of the matrix having 28 elements.


Take m = 7 and n = 4.


Then, m × n = 7 × 4 (=28)


7 × 4 is a possible order of the matrix having 28 elements.


Take m = 14 and n = 2.


Then, m × n = 14 × 2 (=28)


14 × 2 is a possible order of the matrix having 28 elements.


Take m = 28 and n = 1.


Then, m × n = 28 × 1 (=28)


28 × 1 is a possible order of the matrix having 28 elements.


Thus, the possible orders of the matrix having 28 elements are


1 × 28, 2 × 14, 4 × 7, 7 × 4, 14 × 2 and 28 × 1


If the matrix had 13 elements, then also we find the possible order in same way.


Here, mn = 13.


Take m and n to be any number, such that, when it is multiplied it gives 13.


Take m = 1 and n = 13.


Then, m × n = 1 × 13 (=13)


1 × 13 is a possible order of the matrix having 13 elements.


Take m = 13 and n = 1.


Then, m × n = 13 × 1 (=13)


13 × 1 is a possible order of the matrix having 13 elements.


Thus, the possible orders of the matrix having 13 elements are


1 × 13 and 13 × 1


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