Answer
414.9k+ views
Hint:
We know the multiplication of rows and columns of a matrix is the number of total entries in the matrix. So if a matrix is of the order\[\left( {m \times n} \right)\], the possible identical elements will be \[mn\]. For example if we take $6$ identical elements we can get \[4\] possible ordered matrices such as \[\left( {6 \times 1} \right), \left( {3 \times 2} \right), \left( {2 \times 3} \right), \left( {1 \times 6} \right)\].
Complete step by step solution:
To find all the possible orders of \[12\] identical elements we have to find all the ordered matrices of a natural number whose product is \[12\].
We have to find the two numbers whose product is $12$.
So the matrices that can be formed are of these orders \[\left( {1 \times 12} \right),\left( {2 \times 6} \right),\left( {3 \times 4} \right),\left( {4 \times 3} \right),\left( {6 \times 2} \right),\left( {12 \times 1} \right)\].
All of them will have the same 12 identical elements.
So, the possible orders it can have is \[6\].
Hence, option (c) is correct.
Note:
The common mistake all we do is sometimes we forget to count the repeating matrices such as $(1 \times 12)$ and $(12 \times 1)$, $(3 \times 4)$ and $(4 \times 3)$, $(2 \times 6)$ and $(12 \times 6)$. In this case rows and columns are interchanging so the matrix formation will be completely different. Hence, if we forget to count the repeating matrices the answer will be \[3\] which is completely wrong. We have to count all the possible matrices that can be formed.
We know the multiplication of rows and columns of a matrix is the number of total entries in the matrix. So if a matrix is of the order\[\left( {m \times n} \right)\], the possible identical elements will be \[mn\]. For example if we take $6$ identical elements we can get \[4\] possible ordered matrices such as \[\left( {6 \times 1} \right), \left( {3 \times 2} \right), \left( {2 \times 3} \right), \left( {1 \times 6} \right)\].
Complete step by step solution:
To find all the possible orders of \[12\] identical elements we have to find all the ordered matrices of a natural number whose product is \[12\].
We have to find the two numbers whose product is $12$.
So the matrices that can be formed are of these orders \[\left( {1 \times 12} \right),\left( {2 \times 6} \right),\left( {3 \times 4} \right),\left( {4 \times 3} \right),\left( {6 \times 2} \right),\left( {12 \times 1} \right)\].
All of them will have the same 12 identical elements.
So, the possible orders it can have is \[6\].
Hence, option (c) is correct.
Note:
The common mistake all we do is sometimes we forget to count the repeating matrices such as $(1 \times 12)$ and $(12 \times 1)$, $(3 \times 4)$ and $(4 \times 3)$, $(2 \times 6)$ and $(12 \times 6)$. In this case rows and columns are interchanging so the matrix formation will be completely different. Hence, if we forget to count the repeating matrices the answer will be \[3\] which is completely wrong. We have to count all the possible matrices that can be formed.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)