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Let T: R4 → R4 be a linear transformation satisfy T3 + 3T2 = 4I, where I is the identity 
  • a)
    one-one but not onto 
  • b)
    non-invertible
  • c)
    onto but not one-one
  • d)
    invertible 
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Let T: R4 → R4 be a linear transformation satisfy T3 + 3T2 = 4I, ...
Here, L.T T : R4 → R4 satisfy 
T3 + 3T2 = 4I, where I is identity transformation one of the eigenvalues of T is I 
⇒ One of eigenvalue of S = T4 + 3T3 – 4I is zero 
⇒ S is non-invertible
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Let T: R4 → R4 be a linear transformation satisfy T3 + 3T2 = 4I, ...
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Let T: R4 → R4 be a linear transformation satisfy T3 + 3T2 = 4I, where I is the identitya)one-one but not ontob)non-invertiblec)onto but not one-oned)invertibleCorrect answer is option 'B'. Can you explain this answer?
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