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The number of all possible matrices of order 3×3 with each entry 0 or 1 is
- a)18
- b)81
- c)512
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The number of all possible matrices of order3×3 with each entry ...
23x3=29=512.
The number of elements in a 3 X 3 matrix is the product 3 X 3=9.
Each element can either be a 0 or a 1.
Given this, the total possible matrices that can be selected is 29=512
Most Upvoted Answer
The number of all possible matrices of order3×3 with each entry ...
A matrix of order 3 x 3 has 9 elements. Now each element can be 0 or 1.
∴ 9 places can be filled up in 2^9 ways
required number of matrices = 2^9
=2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
=512
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Community Answer
The number of all possible matrices of order3×3 with each entry ...
Understanding Matrix Order
A matrix of order 3×3 has 3 rows and 3 columns. Therefore, it consists of a total of 9 entries.
Possible Entries
Each entry in the matrix can either be a 0 or a 1. This gives us 2 choices (0 or 1) for each of the 9 positions in the matrix.
Calculating Total Combinations
To find the total number of possible matrices, we can use the concept of permutations since each entry is independent of the others. The total number of combinations can be calculated as:
- Number of choices per entry: 2 (either 0 or 1)
- Total entries: 9
Thus, the formula for the total number of matrices is:
Total Matrices = 2^(Number of entries)
Substituting the values:
Total Matrices = 2^9
Calculating 2^9
Now, we calculate 2 raised to the power of 9:
- 2^9 = 512
Conclusion
Therefore, the total number of possible matrices of order 3×3 with each entry being either 0 or 1 is 512.
The correct answer is indeed option 'C', which is 512.
A matrix of order 3×3 has 3 rows and 3 columns. Therefore, it consists of a total of 9 entries.
Possible Entries
Each entry in the matrix can either be a 0 or a 1. This gives us 2 choices (0 or 1) for each of the 9 positions in the matrix.
Calculating Total Combinations
To find the total number of possible matrices, we can use the concept of permutations since each entry is independent of the others. The total number of combinations can be calculated as:
- Number of choices per entry: 2 (either 0 or 1)
- Total entries: 9
Thus, the formula for the total number of matrices is:
Total Matrices = 2^(Number of entries)
Substituting the values:
Total Matrices = 2^9
Calculating 2^9
Now, we calculate 2 raised to the power of 9:
- 2^9 = 512
Conclusion
Therefore, the total number of possible matrices of order 3×3 with each entry being either 0 or 1 is 512.
The correct answer is indeed option 'C', which is 512.
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