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Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of A consisting of all determinants with value –1. Then
- a)C is empty
- b)B has as many elements as C
- c)A = B∪C
- d)B has twice as many elements as elements as C
Correct answer is option 'B'. Can you explain this answer?
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Consider the set A of all determinants of order 3 with entries 0 or 1 ...
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Consider the set A of all determinants of order 3 with entries 0 or 1 ...
To find the set B, we need to find all the determinants of order 3 with entries 0 or 1 that have a value of 1.
We can start by considering the possible patterns of 0's and 1's in a 3x3 matrix that would result in a determinant of 1. One such pattern is:
1 0 0
0 1 0
0 0 1
This matrix has a determinant of 1. However, we can also change the order of the rows or columns and still have a determinant of 1. So, the following matrices also have determinants of 1:
0 0 1
1 0 0
0 1 0
0 1 0
0 0 1
1 0 0
0 1 0
1 0 0
0 0 1
1 0 0
0 0 1
0 1 0
1 0 0
0 1 0
0 0 1
1 0 0
0 1 0
0 0 1
So, the set B consists of these 6 matrices.
Now, let's consider the set C, which consists of all determinants with value 0. To find these matrices, we need to find all patterns of 0's and 1's in a 3x3 matrix that would result in a determinant of 0.
One such pattern is:
1 1 0
0 1 0
0 0 0
This matrix has a determinant of 0. However, we can also change the order of the rows or columns and still have a determinant of 0. So, the following matrices also have determinants of 0:
0 0 0
0 1 0
1 1 0
0 1 0
0 0 0
1 1 0
0 1 0
1 1 0
0 0 0
0 0 0
1 1 0
0 1 0
1 1 0
0 0 0
0 1 0
1 1 0
0 1 0
0 0 0
So, the set C consists of these 6 matrices.
In summary, the set B consists of 6 matrices with determinants of 1, and the set C consists of 6 matrices with determinants of 0.
We can start by considering the possible patterns of 0's and 1's in a 3x3 matrix that would result in a determinant of 1. One such pattern is:
1 0 0
0 1 0
0 0 1
This matrix has a determinant of 1. However, we can also change the order of the rows or columns and still have a determinant of 1. So, the following matrices also have determinants of 1:
0 0 1
1 0 0
0 1 0
0 1 0
0 0 1
1 0 0
0 1 0
1 0 0
0 0 1
1 0 0
0 0 1
0 1 0
1 0 0
0 1 0
0 0 1
1 0 0
0 1 0
0 0 1
So, the set B consists of these 6 matrices.
Now, let's consider the set C, which consists of all determinants with value 0. To find these matrices, we need to find all patterns of 0's and 1's in a 3x3 matrix that would result in a determinant of 0.
One such pattern is:
1 1 0
0 1 0
0 0 0
This matrix has a determinant of 0. However, we can also change the order of the rows or columns and still have a determinant of 0. So, the following matrices also have determinants of 0:
0 0 0
0 1 0
1 1 0
0 1 0
0 0 0
1 1 0
0 1 0
1 1 0
0 0 0
0 0 0
1 1 0
0 1 0
1 1 0
0 0 0
0 1 0
1 1 0
0 1 0
0 0 0
So, the set C consists of these 6 matrices.
In summary, the set B consists of 6 matrices with determinants of 1, and the set C consists of 6 matrices with determinants of 0.
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Consider the set A of all determinants of order 3 with entries 0 or 1 ...
Correct answer is option.B
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Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of A consisting of all determinants with value –1. Thena)C is emptyb)B has as many elements as Cc)A = B∪Cd)B has twice as many elements as elements as CCorrect answer is option 'B'. Can you explain this answer?
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Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of A consisting of all determinants with value –1. Thena)C is emptyb)B has as many elements as Cc)A = B∪Cd)B has twice as many elements as elements as CCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of A consisting of all determinants with value –1. Thena)C is emptyb)B has as many elements as Cc)A = B∪Cd)B has twice as many elements as elements as CCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of A consisting of all determinants with value –1. Thena)C is emptyb)B has as many elements as Cc)A = B∪Cd)B has twice as many elements as elements as CCorrect answer is option 'B'. Can you explain this answer?.
Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of A consisting of all determinants with value –1. Thena)C is emptyb)B has as many elements as Cc)A = B∪Cd)B has twice as many elements as elements as CCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of A consisting of all determinants with value –1. Thena)C is emptyb)B has as many elements as Cc)A = B∪Cd)B has twice as many elements as elements as CCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of A consisting of all determinants with value –1. Thena)C is emptyb)B has as many elements as Cc)A = B∪Cd)B has twice as many elements as elements as CCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of A consisting of all determinants with value –1. Thena)C is emptyb)B has as many elements as Cc)A = B∪Cd)B has twice as many elements as elements as CCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of A consisting of all determinants with value –1. Thena)C is emptyb)B has as many elements as Cc)A = B∪Cd)B has twice as many elements as elements as CCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of A consisting of all determinants with value –1. Thena)C is emptyb)B has as many elements as Cc)A = B∪Cd)B has twice as many elements as elements as CCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of A consisting of all determinants with value –1. Thena)C is emptyb)B has as many elements as Cc)A = B∪Cd)B has twice as many elements as elements as CCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of A consisting of all determinants with value –1. Thena)C is emptyb)B has as many elements as Cc)A = B∪Cd)B has twice as many elements as elements as CCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
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