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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): If every element of a third order determinant of value D is multiplied by 5, then the value of the new determinant is 125D.
Reason (R): If k is a scalar and A is an n × n matrix, then |kA|= kn |A|
- a)Both A and R are true and R is the correct explanation of A
- b)Both A and R are true but R is NOT the correct explanation of A
- c)A is true but R is false
- d)A is false and R is True
Correct answer is option 'A'. Can you explain this answer?
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Directions: In the following questions, A statement of Assertion (A) ...
If k is a scalar and A is an n × n matrix, then |kA| = kn|A|.
This is a property of the determinant. Hence R is true.
Using this property, |5?| = 53 ? = 125?
Hence A is true.
R is the correct explanation of A.
Most Upvoted Answer
Directions: In the following questions, A statement of Assertion (A) ...
Assertion and Reason Explanation:
Assertion (A):
- When every element of a third-order determinant of value D is multiplied by 5, the new determinant's value becomes 125D.
Reason (R):
- The determinant value of a scalar multiple of a matrix is equal to the determinant of the original matrix raised to the power of the number of rows/columns times the scalar.
Explanation:
- The assertion is true because when each element of a determinant is multiplied by a scalar, the determinant's value is also multiplied by that scalar raised to the power of the determinant's order. In this case, 5^3 = 125, hence the new determinant's value is 125D.
- The reason is also true as it explains the concept of determinant transformation under scalar multiplication. The determinant of kA is equal to k^n times the determinant of A, where k is a scalar and A is an n x n matrix.
Therefore, both the assertion and reason are true, and the reason correctly explains why the assertion is true. Hence, the correct answer is option 'A'.
Assertion (A):
- When every element of a third-order determinant of value D is multiplied by 5, the new determinant's value becomes 125D.
Reason (R):
- The determinant value of a scalar multiple of a matrix is equal to the determinant of the original matrix raised to the power of the number of rows/columns times the scalar.
Explanation:
- The assertion is true because when each element of a determinant is multiplied by a scalar, the determinant's value is also multiplied by that scalar raised to the power of the determinant's order. In this case, 5^3 = 125, hence the new determinant's value is 125D.
- The reason is also true as it explains the concept of determinant transformation under scalar multiplication. The determinant of kA is equal to k^n times the determinant of A, where k is a scalar and A is an n x n matrix.
Therefore, both the assertion and reason are true, and the reason correctly explains why the assertion is true. Hence, the correct answer is option 'A'.
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If every element of a third order determinant of value D is multiplied by 5, then the value of the new determinant is 125D.Reason (R): If k is a scalar and A is an n × n matrix, then |kA|= kn |A|a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer?
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Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If every element of a third order determinant of value D is multiplied by 5, then the value of the new determinant is 125D.Reason (R): If k is a scalar and A is an n × n matrix, then |kA|= kn |A|a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. 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 Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If every element of a third order determinant of value D is multiplied by 5, then the value of the new determinant is 125D.Reason (R): If k is a scalar and A is an n × n matrix, then |kA|= kn |A|a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If every element of a third order determinant of value D is multiplied by 5, then the value of the new determinant is 125D.Reason (R): If k is a scalar and A is an n × n matrix, then |kA|= kn |A|a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer?.
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If every element of a third order determinant of value D is multiplied by 5, then the value of the new determinant is 125D.Reason (R): If k is a scalar and A is an n × n matrix, then |kA|= kn |A|a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. 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 Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If every element of a third order determinant of value D is multiplied by 5, then the value of the new determinant is 125D.Reason (R): If k is a scalar and A is an n × n matrix, then |kA|= kn |A|a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If every element of a third order determinant of value D is multiplied by 5, then the value of the new determinant is 125D.Reason (R): If k is a scalar and A is an n × n matrix, then |kA|= kn |A|a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer?.
Solutions for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If every element of a third order determinant of value D is multiplied by 5, then the value of the new determinant is 125D.Reason (R): If k is a scalar and A is an n × n matrix, then |kA|= kn |A|a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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Here you can find the meaning of Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If every element of a third order determinant of value D is multiplied by 5, then the value of the new determinant is 125D.Reason (R): If k is a scalar and A is an n × n matrix, then |kA|= kn |A|a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If every element of a third order determinant of value D is multiplied by 5, then the value of the new determinant is 125D.Reason (R): If k is a scalar and A is an n × n matrix, then |kA|= kn |A|a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If every element of a third order determinant of value D is multiplied by 5, then the value of the new determinant is 125D.Reason (R): If k is a scalar and A is an n × n matrix, then |kA|= kn |A|a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If every element of a third order determinant of value D is multiplied by 5, then the value of the new determinant is 125D.Reason (R): If k is a scalar and A is an n × n matrix, then |kA|= kn |A|a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Directions: In the following questions, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.Assertion (A): If every element of a third order determinant of value D is multiplied by 5, then the value of the new determinant is 125D.Reason (R): If k is a scalar and A is an n × n matrix, then |kA|= kn |A|a)Both A and R are true and R is the correct explanation of Ab)Both A and R are true but R is NOT the correct explanation of Ac)A is true but R is falsed)A is false and R is TrueCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
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