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If |A| represents the determinant of a square matrix of order 3 then (-2A)=
- a)-8|A|
- b)8|A|
- c)-2|A|
- d)2|A|
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If |A| represents the determinant of a square matrix of order 3 then (...
Understanding Determinants and Matrix Scaling
When dealing with the determinant of a matrix, especially in the context of scaling a square matrix, it is essential to understand how the determinant behaves under scalar multiplication.
Determinant of a Matrix
- The determinant of a square matrix, denoted as |A|, is a scalar value that provides important properties about the matrix, including whether it is invertible.
- For a 3x3 matrix, the determinant can be calculated using specific formulas involving the elements of the matrix.
Effect of Scalar Multiplication
- When a square matrix A of order n is multiplied by a scalar k, the effect on the determinant is given by the formula:
|kA| = k^n * |A|
- Here, n is the order of the matrix (in this case, n = 3) and k is the scalar value.
Applying the Formula
- In the case of (-2A), the scalar is -2.
- Therefore, we apply the formula:
|(-2A)| = (-2)^3 * |A|
- Calculating this gives:
|(-2A)| = -8 * |A|
Conclusion
- Hence, the determinant of the matrix (-2A) is -8 times the determinant of the original matrix A.
- This leads us to the correct answer: option (a) - 8|A|.
Understanding this concept is crucial for solving problems related to matrix determinants, especially in competitive exams like JEE.
When dealing with the determinant of a matrix, especially in the context of scaling a square matrix, it is essential to understand how the determinant behaves under scalar multiplication.
Determinant of a Matrix
- The determinant of a square matrix, denoted as |A|, is a scalar value that provides important properties about the matrix, including whether it is invertible.
- For a 3x3 matrix, the determinant can be calculated using specific formulas involving the elements of the matrix.
Effect of Scalar Multiplication
- When a square matrix A of order n is multiplied by a scalar k, the effect on the determinant is given by the formula:
|kA| = k^n * |A|
- Here, n is the order of the matrix (in this case, n = 3) and k is the scalar value.
Applying the Formula
- In the case of (-2A), the scalar is -2.
- Therefore, we apply the formula:
|(-2A)| = (-2)^3 * |A|
- Calculating this gives:
|(-2A)| = -8 * |A|
Conclusion
- Hence, the determinant of the matrix (-2A) is -8 times the determinant of the original matrix A.
- This leads us to the correct answer: option (a) - 8|A|.
Understanding this concept is crucial for solving problems related to matrix determinants, especially in competitive exams like JEE.
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If |A| represents the determinant of a square matrix of order 3 then (-2A)=a)-8|A|b)8|A|c)-2|A|d)2|A|Correct answer is option 'A'. Can you explain this answer? for JEE 2026 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If |A| represents the determinant of a square matrix of order 3 then (-2A)=a)-8|A|b)8|A|c)-2|A|d)2|A|Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If |A| represents the determinant of a square matrix of order 3 then (-2A)=a)-8|A|b)8|A|c)-2|A|d)2|A|Correct answer is option 'A'. Can you explain this answer?.
If |A| represents the determinant of a square matrix of order 3 then (-2A)=a)-8|A|b)8|A|c)-2|A|d)2|A|Correct answer is option 'A'. Can you explain this answer? for JEE 2026 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If |A| represents the determinant of a square matrix of order 3 then (-2A)=a)-8|A|b)8|A|c)-2|A|d)2|A|Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If |A| represents the determinant of a square matrix of order 3 then (-2A)=a)-8|A|b)8|A|c)-2|A|d)2|A|Correct answer is option 'A'. Can you explain this answer?.
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