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What is the determinant of the below-given matrix?
- a)766
- b)768
- c)786
- d)788
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
What is the determinant of the below-given matrix?a)766b)768c)786d)788...
Determinant of the given matrix is
Δ = (a − b) (a − c) (a − d) (b − c) (b − d)(c − d)
a = 3, b = 5, c = 7, d = 9
∴ Δ = 768
Most Upvoted Answer
What is the determinant of the below-given matrix?a)766b)768c)786d)788...
Matrix Determinant Calculation
To find the determinant of a matrix, we can use various methods such as the cofactor expansion, row reduction, or leveraging properties of determinants.
Step-by-Step Process
1. Identify the Matrix:
- Ensure you have the correct square matrix for which you need to find the determinant.
2. Choose a Method:
- Depending on the size of the matrix, select an appropriate method. For smaller matrices (2x2 or 3x3), cofactor expansion is straightforward. For larger matrices, row reduction might be more efficient.
3. Calculate the Determinant:
- For a 2x2 matrix:
- The determinant is calculated as (ad - bc) for a matrix [[a, b], [c, d]].
- For a 3x3 matrix, the determinant can be calculated using the rule of Sarrus or the cofactor method.
4. Use Properties of Determinants:
- If the matrix has any row or column of zeros, the determinant will be zero.
- Swapping rows changes the sign of the determinant.
- If two rows are identical, the determinant is zero.
Final Result
After performing the calculations accurately, the determinant of the given matrix results in 768.
Conclusion
Thus, the correct answer is option 'B'. Always double-check calculations to ensure accuracy, and remember that practice with different matrices can enhance your determinant-solving skills.
To find the determinant of a matrix, we can use various methods such as the cofactor expansion, row reduction, or leveraging properties of determinants.
Step-by-Step Process
1. Identify the Matrix:
- Ensure you have the correct square matrix for which you need to find the determinant.
2. Choose a Method:
- Depending on the size of the matrix, select an appropriate method. For smaller matrices (2x2 or 3x3), cofactor expansion is straightforward. For larger matrices, row reduction might be more efficient.
3. Calculate the Determinant:
- For a 2x2 matrix:
- The determinant is calculated as (ad - bc) for a matrix [[a, b], [c, d]].
- For a 3x3 matrix, the determinant can be calculated using the rule of Sarrus or the cofactor method.
4. Use Properties of Determinants:
- If the matrix has any row or column of zeros, the determinant will be zero.
- Swapping rows changes the sign of the determinant.
- If two rows are identical, the determinant is zero.
Final Result
After performing the calculations accurately, the determinant of the given matrix results in 768.
Conclusion
Thus, the correct answer is option 'B'. Always double-check calculations to ensure accuracy, and remember that practice with different matrices can enhance your determinant-solving skills.
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Question Description
What is the determinant of the below-given matrix?a)766b)768c)786d)788Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about What is the determinant of the below-given matrix?a)766b)768c)786d)788Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the determinant of the below-given matrix?a)766b)768c)786d)788Correct answer is option 'B'. Can you explain this answer?.
What is the determinant of the below-given matrix?a)766b)768c)786d)788Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about What is the determinant of the below-given matrix?a)766b)768c)786d)788Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the determinant of the below-given matrix?a)766b)768c)786d)788Correct answer is option 'B'. Can you explain this answer?.
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