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Consider the following statements about the linear dependence of the real valued functions y1 = 1, y2 = x and y3 = x2, over the field of real numbers.
I. y1, y2 and y3 are linearly independent on – 1 ≤ x ≤ 0
II. y1, y2 and y3 are linearly dependent on 0 ≤ x ≤ 1
III. y1, y2 and y3 are linearly independent on 0 ≤ x ≤ 1
IV. y1, y2 and y3 are linearly dependent on – 1 ≤ x ≤ 0
Which one among the following is correct?
  • a)
    Both I and II are true
  • b)
    Both I and III are true
  • c)
    Both II and IV are true
  • d)
    Both III and IV are true
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Consider the following statements about the linear dependence of the r...
Concept:
The linear dependency or Independency of function fi can be found using Wronskion Matrix.
An analytic function is linearly dependent if:

Application:

Determinant ≠ 0
Function y1, y2, y­3 are linearly independent.
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Community Answer
Consider the following statements about the linear dependence of the r...
False.

The statement is false because y3 can be written as a linear combination of y2 and y1. We have y3 = x^2 = x * x = y2 * y2. Therefore, y3 is not linearly independent from y1 and y2.
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Consider the following statements about the linear dependence of the real valued functions y1= 1, y2= x and y3= x2, over the field of real numbers.I. y1, y2and y3are linearly independent on – 1 ≤ x ≤ 0II. y1, y2and y3are linearly dependent on 0 ≤ x ≤ 1III. y1, y2and y3are linearly independent on 0 ≤ x ≤ 1IV. y1, y2and y3are linearly dependent on – 1 ≤ x ≤ 0Which one among the following is correct?a)Both I and II are trueb)Both I and III are truec)Both II and IV are trued)Both III and IV are trueCorrect answer is option 'B'. Can you explain this answer?
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Consider the following statements about the linear dependence of the real valued functions y1= 1, y2= x and y3= x2, over the field of real numbers.I. y1, y2and y3are linearly independent on – 1 ≤ x ≤ 0II. y1, y2and y3are linearly dependent on 0 ≤ x ≤ 1III. y1, y2and y3are linearly independent on 0 ≤ x ≤ 1IV. y1, y2and y3are linearly dependent on – 1 ≤ x ≤ 0Which one among the following is correct?a)Both I and II are trueb)Both I and III are truec)Both II and IV are trued)Both III and IV are trueCorrect answer is option 'B'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Consider the following statements about the linear dependence of the real valued functions y1= 1, y2= x and y3= x2, over the field of real numbers.I. y1, y2and y3are linearly independent on – 1 ≤ x ≤ 0II. y1, y2and y3are linearly dependent on 0 ≤ x ≤ 1III. y1, y2and y3are linearly independent on 0 ≤ x ≤ 1IV. y1, y2and y3are linearly dependent on – 1 ≤ x ≤ 0Which one among the following is correct?a)Both I and II are trueb)Both I and III are truec)Both II and IV are trued)Both III and IV are trueCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following statements about the linear dependence of the real valued functions y1= 1, y2= x and y3= x2, over the field of real numbers.I. y1, y2and y3are linearly independent on – 1 ≤ x ≤ 0II. y1, y2and y3are linearly dependent on 0 ≤ x ≤ 1III. y1, y2and y3are linearly independent on 0 ≤ x ≤ 1IV. y1, y2and y3are linearly dependent on – 1 ≤ x ≤ 0Which one among the following is correct?a)Both I and II are trueb)Both I and III are truec)Both II and IV are trued)Both III and IV are trueCorrect answer is option 'B'. Can you explain this answer?.
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