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Which of the following statement is incorrect?
- a)Transposition leaves the values of the determinant unchanged.
- b)If two rows of a determinant are proportional, the value of the determinat is zero
- c)If two rows of a determinant are interchanged, the value of the determinant so obtained is same as the value of the original determinant
- d)If the elements of any row of a determinant are multiplied by the same number k (say), then the value of the determinant so obtained is k times the value of the original determinant
Correct answer is option 'C'. Can you explain this answer?
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Which of the following statement is incorrect?a)Transposition leaves t...
Incorrect Statement: If two rows of a determinant are interchanged, the value of the determinant so obtained is the same as the value of the original determinant.
Explanation:
To understand why this statement is incorrect, let's first review the properties of determinants.
Properties of Determinants:
1. Transposition Property: Transposing a determinant means interchanging its rows and columns. The value of the determinant remains unchanged under transposition.
2. Scalar Multiplication Property: If all the elements of a row (or column) of a determinant are multiplied by a scalar k, then the value of the determinant becomes k times the value of the original determinant.
3. Row Multiplication Property: If the elements of any row of a determinant are multiplied by the same number k, then the value of the determinant so obtained is k times the value of the original determinant.
4. Row Interchange Property: If two rows of a determinant are interchanged, the sign of the determinant changes. Specifically, the value of the determinant becomes the negative of the original determinant.
Explanation of Incorrect Statement:
The incorrect statement in option C suggests that if two rows of a determinant are interchanged, the value of the determinant remains the same. However, this is not true. When two rows are interchanged, the sign of the determinant changes, resulting in a different value.
Let's consider a simple example to illustrate this:
Original determinant:
| 1 2 |
| 3 4 |
Interchanging the rows:
| 3 4 |
| 1 2 |
The original determinant has a value of (1*4 - 2*3) = -2.
After interchanging the rows, the new determinant has a value of (3*2 - 4*1) = 2.
Hence, the value of the determinant changes when two rows are interchanged, contradicting the statement in option C.
Conclusion:
The correct answer is option C, which states that if two rows of a determinant are interchanged, the value of the determinant so obtained is the same as the value of the original determinant.
Explanation:
To understand why this statement is incorrect, let's first review the properties of determinants.
Properties of Determinants:
1. Transposition Property: Transposing a determinant means interchanging its rows and columns. The value of the determinant remains unchanged under transposition.
2. Scalar Multiplication Property: If all the elements of a row (or column) of a determinant are multiplied by a scalar k, then the value of the determinant becomes k times the value of the original determinant.
3. Row Multiplication Property: If the elements of any row of a determinant are multiplied by the same number k, then the value of the determinant so obtained is k times the value of the original determinant.
4. Row Interchange Property: If two rows of a determinant are interchanged, the sign of the determinant changes. Specifically, the value of the determinant becomes the negative of the original determinant.
Explanation of Incorrect Statement:
The incorrect statement in option C suggests that if two rows of a determinant are interchanged, the value of the determinant remains the same. However, this is not true. When two rows are interchanged, the sign of the determinant changes, resulting in a different value.
Let's consider a simple example to illustrate this:
Original determinant:
| 1 2 |
| 3 4 |
Interchanging the rows:
| 3 4 |
| 1 2 |
The original determinant has a value of (1*4 - 2*3) = -2.
After interchanging the rows, the new determinant has a value of (3*2 - 4*1) = 2.
Hence, the value of the determinant changes when two rows are interchanged, contradicting the statement in option C.
Conclusion:
The correct answer is option C, which states that if two rows of a determinant are interchanged, the value of the determinant so obtained is the same as the value of the original determinant.
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Which of the following statement is incorrect?a)Transposition leaves the values of the determinant unchanged.b)If two rows of a determinant are proportional, the value of the determinat is zeroc)If two rows of a determinant are interchanged, the value of the determinant so obtained is same as the value of the original determinantd)If the elements of any row of a determinant are multiplied by the same number k (say), then the value of the determinant so obtained is k times the value of the original determinantCorrect answer is option 'C'. Can you explain this answer?
Question Description
Which of the following statement is incorrect?a)Transposition leaves the values of the determinant unchanged.b)If two rows of a determinant are proportional, the value of the determinat is zeroc)If two rows of a determinant are interchanged, the value of the determinant so obtained is same as the value of the original determinantd)If the elements of any row of a determinant are multiplied by the same number k (say), then the value of the determinant so obtained is k times the value of the original determinantCorrect answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Which of the following statement is incorrect?a)Transposition leaves the values of the determinant unchanged.b)If two rows of a determinant are proportional, the value of the determinat is zeroc)If two rows of a determinant are interchanged, the value of the determinant so obtained is same as the value of the original determinantd)If the elements of any row of a determinant are multiplied by the same number k (say), then the value of the determinant so obtained is k times the value of the original determinantCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statement is incorrect?a)Transposition leaves the values of the determinant unchanged.b)If two rows of a determinant are proportional, the value of the determinat is zeroc)If two rows of a determinant are interchanged, the value of the determinant so obtained is same as the value of the original determinantd)If the elements of any row of a determinant are multiplied by the same number k (say), then the value of the determinant so obtained is k times the value of the original determinantCorrect answer is option 'C'. Can you explain this answer?.
Which of the following statement is incorrect?a)Transposition leaves the values of the determinant unchanged.b)If two rows of a determinant are proportional, the value of the determinat is zeroc)If two rows of a determinant are interchanged, the value of the determinant so obtained is same as the value of the original determinantd)If the elements of any row of a determinant are multiplied by the same number k (say), then the value of the determinant so obtained is k times the value of the original determinantCorrect answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Which of the following statement is incorrect?a)Transposition leaves the values of the determinant unchanged.b)If two rows of a determinant are proportional, the value of the determinat is zeroc)If two rows of a determinant are interchanged, the value of the determinant so obtained is same as the value of the original determinantd)If the elements of any row of a determinant are multiplied by the same number k (say), then the value of the determinant so obtained is k times the value of the original determinantCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statement is incorrect?a)Transposition leaves the values of the determinant unchanged.b)If two rows of a determinant are proportional, the value of the determinat is zeroc)If two rows of a determinant are interchanged, the value of the determinant so obtained is same as the value of the original determinantd)If the elements of any row of a determinant are multiplied by the same number k (say), then the value of the determinant so obtained is k times the value of the original determinantCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Which of the following statement is incorrect?a)Transposition leaves the values of the determinant unchanged.b)If two rows of a determinant are proportional, the value of the determinat is zeroc)If two rows of a determinant are interchanged, the value of the determinant so obtained is same as the value of the original determinantd)If the elements of any row of a determinant are multiplied by the same number k (say), then the value of the determinant so obtained is k times the value of the original determinantCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics.
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Which of the following statement is incorrect?a)Transposition leaves the values of the determinant unchanged.b)If two rows of a determinant are proportional, the value of the determinat is zeroc)If two rows of a determinant are interchanged, the value of the determinant so obtained is same as the value of the original determinantd)If the elements of any row of a determinant are multiplied by the same number k (say), then the value of the determinant so obtained is k times the value of the original determinantCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Which of the following statement is incorrect?a)Transposition leaves the values of the determinant unchanged.b)If two rows of a determinant are proportional, the value of the determinat is zeroc)If two rows of a determinant are interchanged, the value of the determinant so obtained is same as the value of the original determinantd)If the elements of any row of a determinant are multiplied by the same number k (say), then the value of the determinant so obtained is k times the value of the original determinantCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Which of the following statement is incorrect?a)Transposition leaves the values of the determinant unchanged.b)If two rows of a determinant are proportional, the value of the determinat is zeroc)If two rows of a determinant are interchanged, the value of the determinant so obtained is same as the value of the original determinantd)If the elements of any row of a determinant are multiplied by the same number k (say), then the value of the determinant so obtained is k times the value of the original determinantCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Which of the following statement is incorrect?a)Transposition leaves the values of the determinant unchanged.b)If two rows of a determinant are proportional, the value of the determinat is zeroc)If two rows of a determinant are interchanged, the value of the determinant so obtained is same as the value of the original determinantd)If the elements of any row of a determinant are multiplied by the same number k (say), then the value of the determinant so obtained is k times the value of the original determinantCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Mathematics tests.
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