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Let  be a linear transform ation satisfying T3 + 3T2 = 4I, where I is  the identity transformation. Then the linear transformation S = T4 + 3T3 - 4I is
  • a)
    One -one but not onto
  • b)
    Onto but not one-one
  • c)
    Invertible
  • d)
    Non-Invertible
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Letbe a linear transform ation satisfying T3 + 3T2 = 4I, where I isthe...
Given
  be a linear transformation,
,  is also a linear transformation, on 
Now S = T4 + 3T3 - 4I is also a linear transformation , on 
⇒ S = T (T3 + 3T2) - 4I = T (4I) - 4I = 4 (T - 1)
Now ker
(S) = ( V ∈ R4 | S(v) = 0)
⇒ 1 is the eigenvalue of T
⇒ ker (S) be the set of eigenvectors corresponding to the eigenvalue 1.
⇒ S is not one -one
⇒ S i s not on to
now clearly 1 is an eigenvalue of T
⇒ S is not invertible
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Most Upvoted Answer
Letbe a linear transform ation satisfying T3 + 3T2 = 4I, where I isthe...
Given
  be a linear transformation,
,  is also a linear transformation, on 
Now S = T4 + 3T3 - 4I is also a linear transformation , on 
⇒ S = T (T3 + 3T2) - 4I = T (4I) - 4I = 4 (T - 1)
Now ker
(S) = ( V ∈ R4 | S(v) = 0)
⇒ 1 is the eigenvalue of T
⇒ ker (S) be the set of eigenvectors corresponding to the eigenvalue 1.
⇒ S is not one -one
⇒ S i s not on to
now clearly 1 is an eigenvalue of T
⇒ S is not invertible
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Letbe a linear transform ation satisfying T3 + 3T2 = 4I, where I isthe identity transformation. Then the linear transformation S = T4 + 3T3 - 4I isa)One -one but not ontob)Onto but not one-onec)Invertibled)Non-InvertibleCorrect answer is option 'D'. Can you explain this answer?
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Letbe a linear transform ation satisfying T3 + 3T2 = 4I, where I isthe identity transformation. Then the linear transformation S = T4 + 3T3 - 4I isa)One -one but not ontob)Onto but not one-onec)Invertibled)Non-InvertibleCorrect answer is option '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 Letbe a linear transform ation satisfying T3 + 3T2 = 4I, where I isthe identity transformation. Then the linear transformation S = T4 + 3T3 - 4I isa)One -one but not ontob)Onto but not one-onec)Invertibled)Non-InvertibleCorrect answer is option '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 Letbe a linear transform ation satisfying T3 + 3T2 = 4I, where I isthe identity transformation. Then the linear transformation S = T4 + 3T3 - 4I isa)One -one but not ontob)Onto but not one-onec)Invertibled)Non-InvertibleCorrect answer is option 'D'. Can you explain this answer?.
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