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Which of the following is one of the criterions for linearity of an equation?
- a)The dependent variable and its derivatives should be of second order
- b)Each coefficient depends only on the independent variable
- c)Each coefficient does not depend on the independent variable
- d)The dependent variable and its derivatives should not be of same order
Correct answer is option 'B'. Can you explain this answer?
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Which of the following is one of the criterions for linearity of an eq...
The two criterions for linearity of an equation are:
- The dependent variable y and its derivatives are of first degree.
- Each coefficient depends only on the independent variable.
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Which of the following is one of the criterions for linearity of an eq...
Linearity of an Equation
The linearity of an equation refers to the property of an equation being linear. A linear equation is an equation in which the variables and their derivatives (if present) have a degree of one. In other words, the power of each variable or its derivative is one.
Criterion for Linearity
Among the given options, option 'B' is the correct criterion for linearity of an equation. Let's understand why.
Explanation
In a linear equation, each coefficient should depend only on the independent variable. This means that the coefficients should not change with respect to other variables or their derivatives.
If a coefficient depends on any other variable or derivative, the equation becomes non-linear. This is because the power of that variable or derivative will be greater than one, breaking the linearity property.
For example, consider the equation: y = mx + c
In this equation, the coefficient 'm' depends only on the independent variable 'x'. It represents the slope of the line and remains constant regardless of any other variables or derivatives. The coefficient 'c' is the y-intercept and also remains constant.
If we have an equation where the coefficients depend on any other variable or its derivative, the equation becomes non-linear. For instance, if we have an equation like y = mx^2 + c, it is no longer linear because the coefficient 'm' depends on the square of the independent variable 'x'.
Therefore, the correct criterion for linearity of an equation is that each coefficient should depend only on the independent variable. Option 'B' satisfies this criterion and is the correct answer.
Conclusion
In summary, the criterion for linearity of an equation is that each coefficient should depend only on the independent variable. This avoids any higher powers or dependencies on other variables or their derivatives. The linearity property is essential in many mathematical and scientific applications, as it simplifies the analysis and solution of equations.
The linearity of an equation refers to the property of an equation being linear. A linear equation is an equation in which the variables and their derivatives (if present) have a degree of one. In other words, the power of each variable or its derivative is one.
Criterion for Linearity
Among the given options, option 'B' is the correct criterion for linearity of an equation. Let's understand why.
Explanation
In a linear equation, each coefficient should depend only on the independent variable. This means that the coefficients should not change with respect to other variables or their derivatives.
If a coefficient depends on any other variable or derivative, the equation becomes non-linear. This is because the power of that variable or derivative will be greater than one, breaking the linearity property.
For example, consider the equation: y = mx + c
In this equation, the coefficient 'm' depends only on the independent variable 'x'. It represents the slope of the line and remains constant regardless of any other variables or derivatives. The coefficient 'c' is the y-intercept and also remains constant.
If we have an equation where the coefficients depend on any other variable or its derivative, the equation becomes non-linear. For instance, if we have an equation like y = mx^2 + c, it is no longer linear because the coefficient 'm' depends on the square of the independent variable 'x'.
Therefore, the correct criterion for linearity of an equation is that each coefficient should depend only on the independent variable. Option 'B' satisfies this criterion and is the correct answer.
Conclusion
In summary, the criterion for linearity of an equation is that each coefficient should depend only on the independent variable. This avoids any higher powers or dependencies on other variables or their derivatives. The linearity property is essential in many mathematical and scientific applications, as it simplifies the analysis and solution of equations.
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Which of the following is one of the criterions for linearity of an equation?a)The dependent variable and its derivatives should be of second orderb)Each coefficient depends only on the independent variablec)Each coefficient does not depend on the independent variabled)The dependent variable and its derivatives should not be of same orderCorrect answer is option 'B'. Can you explain this answer?
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Which of the following is one of the criterions for linearity of an equation?a)The dependent variable and its derivatives should be of second orderb)Each coefficient depends only on the independent variablec)Each coefficient does not depend on the independent variabled)The dependent variable and its derivatives should not be of same orderCorrect answer is option 'B'. 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 is one of the criterions for linearity of an equation?a)The dependent variable and its derivatives should be of second orderb)Each coefficient depends only on the independent variablec)Each coefficient does not depend on the independent variabled)The dependent variable and its derivatives should not be of same orderCorrect answer is option 'B'. 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 is one of the criterions for linearity of an equation?a)The dependent variable and its derivatives should be of second orderb)Each coefficient depends only on the independent variablec)Each coefficient does not depend on the independent variabled)The dependent variable and its derivatives should not be of same orderCorrect answer is option 'B'. Can you explain this answer?.
Which of the following is one of the criterions for linearity of an equation?a)The dependent variable and its derivatives should be of second orderb)Each coefficient depends only on the independent variablec)Each coefficient does not depend on the independent variabled)The dependent variable and its derivatives should not be of same orderCorrect answer is option 'B'. 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 is one of the criterions for linearity of an equation?a)The dependent variable and its derivatives should be of second orderb)Each coefficient depends only on the independent variablec)Each coefficient does not depend on the independent variabled)The dependent variable and its derivatives should not be of same orderCorrect answer is option 'B'. 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 is one of the criterions for linearity of an equation?a)The dependent variable and its derivatives should be of second orderb)Each coefficient depends only on the independent variablec)Each coefficient does not depend on the independent variabled)The dependent variable and its derivatives should not be of same orderCorrect answer is option 'B'. Can you explain this answer?.
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