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Let V be a vector space and T transformation from V to V. then the intersection of the range of T and the null space of T is the zero subspace from of V if and only if.
  • a)
    range of T is different from the nullity of T
  • b)
    T(x) = 0 ⇒ x = 0
  • c)
    T(T(x)) = 0 = ⇒ x = 0
  • d)
    T(T(x)) = 0 ⇒ T(x) = 0
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Let V be a vector space and T transformation from V to V. then the int...
Let R(T) = Range of T
N(T) = null space of T
Let R(T)∩,N(T) = {0}
⇒ R(T) and N(T) both are disjoint subspaces of V.
Now if T(T(x)) = 0, where T(x) ∈ R(T)
⇒ T(x)∈N(T)
⇒ T(x) = 0
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Most Upvoted Answer
Let V be a vector space and T transformation from V to V. then the int...
The correct answer is:

a) range of T is different from the nullity of T
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Community Answer
Let V be a vector space and T transformation from V to V. then the int...
If M is a7×5 matrix of rank 3 and M is a 5×7matrix of rank 5,then rank (MN) is
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Let V be a vector space and T transformation from V to V. then the intersection of the range of T and the null space of T is the zero subspace from of V if and only if.a)range of T is different from the nullity of Tb)T(x) = 0 ⇒ x = 0c)T(T(x)) = 0 = ⇒ x = 0d)T(T(x)) = 0 ⇒ T(x) = 0Correct answer is option 'D'. Can you explain this answer?
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Let V be a vector space and T transformation from V to V. then the intersection of the range of T and the null space of T is the zero subspace from of V if and only if.a)range of T is different from the nullity of Tb)T(x) = 0 ⇒ x = 0c)T(T(x)) = 0 = ⇒ x = 0d)T(T(x)) = 0 ⇒ T(x) = 0Correct 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 Let V be a vector space and T transformation from V to V. then the intersection of the range of T and the null space of T is the zero subspace from of V if and only if.a)range of T is different from the nullity of Tb)T(x) = 0 ⇒ x = 0c)T(T(x)) = 0 = ⇒ x = 0d)T(T(x)) = 0 ⇒ T(x) = 0Correct 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 Let V be a vector space and T transformation from V to V. then the intersection of the range of T and the null space of T is the zero subspace from of V if and only if.a)range of T is different from the nullity of Tb)T(x) = 0 ⇒ x = 0c)T(T(x)) = 0 = ⇒ x = 0d)T(T(x)) = 0 ⇒ T(x) = 0Correct answer is option 'D'. Can you explain this answer?.
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