Answer
Verified
333.6k+ views
Hint: Calculate the number of elements that can be there in the matrix of order 2 $\times $ 3. These elements can have only 0 or 1. Using the concept of permutations and combinations to find the number of all possible matrices of order 2 $\times $ 3 with each entry 0 or 1.
Complete step-by-step answer:
Before proceeding with the question, we must know all the formulas that will be required to solve this question.
In matrices, if we have a matrix of order m $\times $ n, then the number of elements in this matrix are equal to mn . . . . . . . . . . . . . . . . (1)
In permutations and combination, by the concept of principle of counting, if there are n places and on each place, we can place m numbers, then, the number of ways in which we can have different numbers is equal to ${{m}^{n}}$. . . . . . . . . . . . . . (2)
In this question, we are given a matrix of order 2 $\times $ 3. Using formula (1), we can say that the number of elements in this matrix is equal to (2)(3) = 6.
Also, in the question, it is given that at every place, the matrix can have either 0 or 1. So, using formula (2), the number of possible matrices is equal to ${{2}^{6}}=64$.
Hence, the answer is 64.
Note: There is a possibility that one may commit a mistake while using the formula (2). It is possible that one may apply the formula ${{n}^{m}}$ instead of the formula ${{m}^{n}}$ which will give us an incorrect answer.
Complete step-by-step answer:
Before proceeding with the question, we must know all the formulas that will be required to solve this question.
In matrices, if we have a matrix of order m $\times $ n, then the number of elements in this matrix are equal to mn . . . . . . . . . . . . . . . . (1)
In permutations and combination, by the concept of principle of counting, if there are n places and on each place, we can place m numbers, then, the number of ways in which we can have different numbers is equal to ${{m}^{n}}$. . . . . . . . . . . . . . (2)
In this question, we are given a matrix of order 2 $\times $ 3. Using formula (1), we can say that the number of elements in this matrix is equal to (2)(3) = 6.
Also, in the question, it is given that at every place, the matrix can have either 0 or 1. So, using formula (2), the number of possible matrices is equal to ${{2}^{6}}=64$.
Hence, the answer is 64.
Note: There is a possibility that one may commit a mistake while using the formula (2). It is possible that one may apply the formula ${{n}^{m}}$ instead of the formula ${{m}^{n}}$ which will give us an incorrect answer.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
Using the following information to help you answer class 12 chemistry CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with proper collective nouns 1 A of class 10 english CBSE
What is the color of ferrous sulphate crystals? How does this color change after heating? Name the products formed on strongly heating ferrous sulphate crystals. What type of chemical reaction occurs in this type of change.
One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Net gain of ATP in glycolysis a 6 b 2 c 4 d 8 class 11 biology CBSE
What organs are located on the left side of your body class 11 biology CBSE