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The number of all possible matrices of order 3×3 with each entry 0 if 1 is
- a)81
- b)512
- c)18
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The number of all possible matrices of order3×3 with each entry ...
To find the number of all possible matrices of order 3, we need to consider the number of choices for each entry in the matrix.
In a matrix of order 3, there are 9 entries. Each entry can be chosen from any number in the set {0, 1, 2, ..., 9} since there are no restrictions mentioned. Therefore, there are 10 choices for each entry.
Since each entry can be chosen independently, we can use the multiplication principle to find the total number of matrices. This principle states that if there are n choices for one event and m choices for another event, then there are n * m choices for both events together.
Applying this principle to our matrix, we have 10 choices for each of the 9 entries. Therefore, the total number of possible matrices of order 3 is 10^9.
Hence, the number of all possible matrices of order 3 is 10^9.
In a matrix of order 3, there are 9 entries. Each entry can be chosen from any number in the set {0, 1, 2, ..., 9} since there are no restrictions mentioned. Therefore, there are 10 choices for each entry.
Since each entry can be chosen independently, we can use the multiplication principle to find the total number of matrices. This principle states that if there are n choices for one event and m choices for another event, then there are n * m choices for both events together.
Applying this principle to our matrix, we have 10 choices for each of the 9 entries. Therefore, the total number of possible matrices of order 3 is 10^9.
Hence, the number of all possible matrices of order 3 is 10^9.
Community Answer
The number of all possible matrices of order3×3 with each entry ...
Here you need to use the PERMUTATION & COMBINATION. It is given that the matrix is of order 3×3 i. e, in total there are 9 empty places for you to fill the elements. And for each place you have only 2 options i. e, 1 or 0. Now use P&C, 9 places 2 elements for each place and repetation is allowed, so no. of combinations = 2^9 = 512
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The number of all possible matrices of order3×3 with each entry 0 if 1 isa)81b)512c)18d)none of theseCorrect answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of all possible matrices of order3×3 with each entry 0 if 1 isa)81b)512c)18d)none of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of all possible matrices of order3×3 with each entry 0 if 1 isa)81b)512c)18d)none of theseCorrect answer is option 'B'. Can you explain this answer?.
The number of all possible matrices of order3×3 with each entry 0 if 1 isa)81b)512c)18d)none of theseCorrect answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The number of all possible matrices of order3×3 with each entry 0 if 1 isa)81b)512c)18d)none of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of all possible matrices of order3×3 with each entry 0 if 1 isa)81b)512c)18d)none of theseCorrect answer is option 'B'. Can you explain this answer?.
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