Mathematics Exam  >  Mathematics Questions  >  Let T be a linear transformation from a vecto... Start Learning for Free
Let T be a linear transformation from a vector space into a vector space with U as finite dimensional. The rank of T is the dimension of the

  • a)
    null space of T 

  • b)
    range of T

  • c)
    vector space U

  • d)
    vector space V

Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Let T be a linear transformation from a vector space into a vector sp...
linear transformations and their properties related to rank. The rank of a linear transformation T from a vector space U into a vector space V is defined as the dimension of the image (or range) of T. This means that the rank of T is the number of dimensions in the image of T, which is the subset of V that consists of all the vectors that can be obtained by applying T to vectors in U.
Therefore, the rank of T corresponds to dimension of the range of T.
View all questions of this test
Most Upvoted Answer
Let T be a linear transformation from a vector space into a vector sp...
Yes option A is correct as the rank determines the number of linearly independent vectors that span the range of the Transformation here the range is the subset of V(F).
rank of T is the number of linearly independent column
s that represent the matrix of the transformation T and by theory of linearly equations we can verify the correctness of the above fact
Free Test
Community Answer
Let T be a linear transformation from a vector space into a vector sp...
A) range of t
B) null space of t
C) vector space u
D) vector space v
Explore Courses for Mathematics exam
Question Description
Let T be a linear transformation from a vector space into a vector space with U as finite dimensional. The rank of T is the dimension of thea)null space of Tb)range of Tc)vector space Ud)vector space VCorrect answer is option 'B'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about Let T be a linear transformation from a vector space into a vector space with U as finite dimensional. The rank of T is the dimension of thea)null space of Tb)range of Tc)vector space Ud)vector space VCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let T be a linear transformation from a vector space into a vector space with U as finite dimensional. The rank of T is the dimension of thea)null space of Tb)range of Tc)vector space Ud)vector space VCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Let T be a linear transformation from a vector space into a vector space with U as finite dimensional. The rank of T is the dimension of thea)null space of Tb)range of Tc)vector space Ud)vector space VCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics. Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of Let T be a linear transformation from a vector space into a vector space with U as finite dimensional. The rank of T is the dimension of thea)null space of Tb)range of Tc)vector space Ud)vector space VCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Let T be a linear transformation from a vector space into a vector space with U as finite dimensional. The rank of T is the dimension of thea)null space of Tb)range of Tc)vector space Ud)vector space VCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Let T be a linear transformation from a vector space into a vector space with U as finite dimensional. The rank of T is the dimension of thea)null space of Tb)range of Tc)vector space Ud)vector space VCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Let T be a linear transformation from a vector space into a vector space with U as finite dimensional. The rank of T is the dimension of thea)null space of Tb)range of Tc)vector space Ud)vector space VCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Let T be a linear transformation from a vector space into a vector space with U as finite dimensional. The rank of T is the dimension of thea)null space of Tb)range of Tc)vector space Ud)vector space VCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Mathematics tests.
Explore Courses for Mathematics exam
Signup to solve all Doubts
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev