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Let  defined by  then, which of the folowing is/are true ?
  • a)
    f and g are linearly independent in [-1,1]
  • b)
    f and g are linearly dependent in [-1,1]
  • c)
    f(x) g’(x) - f'(x) g(x) is not identically zero on [-1,1]
  • d)
    f(x) g ’(x) - f ’(x) g(x) is identically z e ro in [-1,1]
Correct answer is option 'A,D'. Can you explain this answer?
Verified Answer
Letdefined bythen, which of the folowing is/are true ?a)f and g are li...
and 
Now if x∈[-1,0] then
if(x) =x3 and g(x)=-x3 => f,g are linearly dependent (vf=(-1)g) 
if x∈ [0,1]then
f( x ) = x3 and g (x)= x3 ⇒ f,g are linearly dependent ( ∵ f = ( 1 ) g )
⇒ f, g are linearly dependent in [-1,0] and [0,1] but they are L.l. in [-1,1] as 
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Most Upvoted Answer
Letdefined bythen, which of the folowing is/are true ?a)f and g are li...
and 
Now if x∈[-1,0] then
if(x) =x3 and g(x)=-x3 => f,g are linearly dependent (vf=(-1)g) 
if x∈ [0,1]then
f( x ) = x3 and g (x)= x3 ⇒ f,g are linearly dependent ( ∵ f = ( 1 ) g )
⇒ f, g are linearly dependent in [-1,0] and [0,1] but they are L.l. in [-1,1] as 
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Letdefined bythen, which of the folowing is/are true ?a)f and g are linearly independent in [-1,1]b)f and g are linearly dependent in [-1,1]c)f(x) g’(x) - f(x) g(x) is not identically zero on [-1,1]d)f(x) g ’(x) - f ’(x) g(x) is identically z e ro in [-1,1]Correct answer is option 'A,D'. Can you explain this answer?
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Letdefined bythen, which of the folowing is/are true ?a)f and g are linearly independent in [-1,1]b)f and g are linearly dependent in [-1,1]c)f(x) g’(x) - f(x) g(x) is not identically zero on [-1,1]d)f(x) g ’(x) - f ’(x) g(x) is identically z e ro in [-1,1]Correct answer is option 'A,D'. 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 Letdefined bythen, which of the folowing is/are true ?a)f and g are linearly independent in [-1,1]b)f and g are linearly dependent in [-1,1]c)f(x) g’(x) - f(x) g(x) is not identically zero on [-1,1]d)f(x) g ’(x) - f ’(x) g(x) is identically z e ro in [-1,1]Correct answer is option 'A,D'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Letdefined bythen, which of the folowing is/are true ?a)f and g are linearly independent in [-1,1]b)f and g are linearly dependent in [-1,1]c)f(x) g’(x) - f(x) g(x) is not identically zero on [-1,1]d)f(x) g ’(x) - f ’(x) g(x) is identically z e ro in [-1,1]Correct answer is option 'A,D'. Can you explain this answer?.
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