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For a positive integer n, let denote the vector space of polynomials in one variable x with real coefficients and with degree < n. Consider the map defined by T (p (x)) = p (x2), then
  • a)
    T is a linear transformation and dim Range(T) = 5
  • b)
    T is a linear transformation and diin(Range (T)) = 3
  • c)
    T is a linear transformation and dim Range (T) = 2
  • d)
    T is not a linear transformation.
Correct answer is option 'B'. Can you explain this answer?
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For a positive integer n,let denote the vector space of polynomials i...
X^2 doesn't have an image (x^4 does not belong in P2[x]). Answer should be D.
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For a positive integer n,let denote the vector space of polynomials in one variable x with real coefficients and with degree < n. Consider the map defined by T (p (x)) = p (x2), thena)T is a linear transformation and dim Range(T) = 5b)T is a linear transformation and diin(Range (T)) = 3c)T is a linear transformation and dim Range (T) = 2d)T is not a linear transformation.Correct answer is option 'B'. Can you explain this answer?
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For a positive integer n,let denote the vector space of polynomials in one variable x with real coefficients and with degree < n. Consider the map defined by T (p (x)) = p (x2), thena)T is a linear transformation and dim Range(T) = 5b)T is a linear transformation and diin(Range (T)) = 3c)T is a linear transformation and dim Range (T) = 2d)T is not a linear transformation.Correct 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 For a positive integer n,let denote the vector space of polynomials in one variable x with real coefficients and with degree < n. Consider the map defined by T (p (x)) = p (x2), thena)T is a linear transformation and dim Range(T) = 5b)T is a linear transformation and diin(Range (T)) = 3c)T is a linear transformation and dim Range (T) = 2d)T is not a linear transformation.Correct 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 For a positive integer n,let denote the vector space of polynomials in one variable x with real coefficients and with degree < n. Consider the map defined by T (p (x)) = p (x2), thena)T is a linear transformation and dim Range(T) = 5b)T is a linear transformation and diin(Range (T)) = 3c)T is a linear transformation and dim Range (T) = 2d)T is not a linear transformation.Correct answer is option 'B'. Can you explain this answer?.
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