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Which one of the following is not a criterion for linearity of an equation?
- a)The dependent variable y should be of second order
- b)Each coefficient does not depend on the independent variable
- c)The derivatives of the dependent variable should be of second order
- d)Each coefficient depends only on the independent variable
Correct answer is option 'B'. Can you explain this answer?
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Which one of the following is not a criterion for linearity of an equa...
The two criterions for linearity of an equation are: The dependent variable y and its derivatives of first degree. Each coefficient depends only on the independent variable.
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Which one of the following is not a criterion for linearity of an equa...
Linearity of an equation
Linearity refers to the property of an equation where the dependent variable changes linearly with the independent variable(s). In other words, a linear equation is one where the relationship between the variables can be represented by a straight line on a graph.
Criteria for linearity
There are certain criteria that need to be satisfied for an equation to be considered linear. These criteria are as follows:
a) The dependent variable y should be of first order: This means that the equation should not involve the dependent variable raised to any power other than 1. For example, y^2 or y^3 would violate this criterion.
b) Each coefficient does not depend on the independent variable: In a linear equation, the coefficients of the variables should be constant values, independent of the values of the independent variable(s). This ensures that the relationship between the variables remains linear.
c) The derivatives of the dependent variable should be of first order: The derivatives of the dependent variable with respect to the independent variable should not involve any higher-order derivatives. For example, if the equation involves the second derivative of y with respect to x, it would violate this criterion.
d) Each coefficient depends only on the independent variable: In a linear equation, the coefficients of the variables should depend only on the independent variable(s) and not on any other variables. This criterion ensures that the relationship between the variables is linear and does not involve any interactions with other variables.
The criterion that is not a requirement for linearity
The criterion that is not a requirement for linearity of an equation is option B, which states that each coefficient does not depend on the independent variable. In a linear equation, the coefficients are constant values that do not change with the values of the independent variable(s). This criterion is essential to maintain linearity because if the coefficients were dependent on the independent variable(s), the relationship between the variables would become nonlinear.
In summary, all the other options listed (a, c, and d) are necessary criteria for linearity of an equation, while option B violates the requirement for linearity.
Linearity refers to the property of an equation where the dependent variable changes linearly with the independent variable(s). In other words, a linear equation is one where the relationship between the variables can be represented by a straight line on a graph.
Criteria for linearity
There are certain criteria that need to be satisfied for an equation to be considered linear. These criteria are as follows:
a) The dependent variable y should be of first order: This means that the equation should not involve the dependent variable raised to any power other than 1. For example, y^2 or y^3 would violate this criterion.
b) Each coefficient does not depend on the independent variable: In a linear equation, the coefficients of the variables should be constant values, independent of the values of the independent variable(s). This ensures that the relationship between the variables remains linear.
c) The derivatives of the dependent variable should be of first order: The derivatives of the dependent variable with respect to the independent variable should not involve any higher-order derivatives. For example, if the equation involves the second derivative of y with respect to x, it would violate this criterion.
d) Each coefficient depends only on the independent variable: In a linear equation, the coefficients of the variables should depend only on the independent variable(s) and not on any other variables. This criterion ensures that the relationship between the variables is linear and does not involve any interactions with other variables.
The criterion that is not a requirement for linearity
The criterion that is not a requirement for linearity of an equation is option B, which states that each coefficient does not depend on the independent variable. In a linear equation, the coefficients are constant values that do not change with the values of the independent variable(s). This criterion is essential to maintain linearity because if the coefficients were dependent on the independent variable(s), the relationship between the variables would become nonlinear.
In summary, all the other options listed (a, c, and d) are necessary criteria for linearity of an equation, while option B violates the requirement for linearity.
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Which one of the following is not a criterion for linearity of an equation?a)The dependent variable y should be of second orderb)Each coefficient does not depend on the independent variablec)The derivatives of the dependent variable should be of second orderd)Each coefficient depends only on the independent variableCorrect answer is option 'B'. Can you explain this answer?
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Which one of the following is not a criterion for linearity of an equation?a)The dependent variable y should be of second orderb)Each coefficient does not depend on the independent variablec)The derivatives of the dependent variable should be of second orderd)Each coefficient depends only on the independent variableCorrect 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 one of the following is not a criterion for linearity of an equation?a)The dependent variable y should be of second orderb)Each coefficient does not depend on the independent variablec)The derivatives of the dependent variable should be of second orderd)Each coefficient depends only on the independent variableCorrect 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 one of the following is not a criterion for linearity of an equation?a)The dependent variable y should be of second orderb)Each coefficient does not depend on the independent variablec)The derivatives of the dependent variable should be of second orderd)Each coefficient depends only on the independent variableCorrect answer is option 'B'. Can you explain this answer?.
Which one of the following is not a criterion for linearity of an equation?a)The dependent variable y should be of second orderb)Each coefficient does not depend on the independent variablec)The derivatives of the dependent variable should be of second orderd)Each coefficient depends only on the independent variableCorrect 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 one of the following is not a criterion for linearity of an equation?a)The dependent variable y should be of second orderb)Each coefficient does not depend on the independent variablec)The derivatives of the dependent variable should be of second orderd)Each coefficient depends only on the independent variableCorrect 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 one of the following is not a criterion for linearity of an equation?a)The dependent variable y should be of second orderb)Each coefficient does not depend on the independent variablec)The derivatives of the dependent variable should be of second orderd)Each coefficient depends only on the independent variableCorrect answer is option 'B'. Can you explain this answer?.
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Which one of the following is not a criterion for linearity of an equation?a)The dependent variable y should be of second orderb)Each coefficient does not depend on the independent variablec)The derivatives of the dependent variable should be of second orderd)Each coefficient depends only on the independent variableCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Which one of the following is not a criterion for linearity of an equation?a)The dependent variable y should be of second orderb)Each coefficient does not depend on the independent variablec)The derivatives of the dependent variable should be of second orderd)Each coefficient depends only on the independent variableCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Which one of the following is not a criterion for linearity of an equation?a)The dependent variable y should be of second orderb)Each coefficient does not depend on the independent variablec)The derivatives of the dependent variable should be of second orderd)Each coefficient depends only on the independent variableCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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