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Consider, the linear transformation
T : R4 ----> R4 given by: 
T(x, y, z, u) = (x, y, 0, 0),
Then, which one of the following is correct?
  • a)
    Rank of T > Nullity of T
  • b)
    Nullity of T > Rank of T
  • c)
    Rank of T = Nullity of T = 3
  • d)
    Rank of T = Nullity of T = 2
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Consider, the linear transformationT : R4 ---->R4 given by:T(x, y, ...
We are given that linear transformation

We need to determine Rank and Nullity of T.
Let (x,y, z, u) ∈ ker T
Then T(x, y, z, u) = (0, 0, 0, 0)
Using the definition of linear transformation we get
(x,y, 0, 0) = (0, 0, 0, 0)
implies x = 0, y = 0, z and u are arbitrary
Therefore,

Hence, Nullity of T = 2
Using Rank Nullity theorem, we get
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Most Upvoted Answer
Consider, the linear transformationT : R4 ---->R4 given by:T(x, y, ...
We are given that linear transformation

We need to determine Rank and Nullity of T.
Let (x,y, z, u) ∈ ker T
Then T(x, y, z, u) = (0, 0, 0, 0)
Using the definition of linear transformation we get
(x,y, 0, 0) = (0, 0, 0, 0)
implies x = 0, y = 0, z and u are arbitrary
Therefore,

Hence, Nullity of T = 2
Using Rank Nullity theorem, we get
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Consider, the linear transformationT : R4 ---->R4 given by:T(x, y, z, u) = (x, y, 0, 0), Then, which one of the following is correct?a)Rank of T > Nullity of Tb)Nullity of T > Rank of Tc)Rank of T = Nullity of T = 3d)Rank of T = Nullity of T = 2Correct answer is option 'D'. Can you explain this answer?
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Consider, the linear transformationT : R4 ---->R4 given by:T(x, y, z, u) = (x, y, 0, 0), Then, which one of the following is correct?a)Rank of T > Nullity of Tb)Nullity of T > Rank of Tc)Rank of T = Nullity of T = 3d)Rank of T = Nullity of T = 2Correct 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 Consider, the linear transformationT : R4 ---->R4 given by:T(x, y, z, u) = (x, y, 0, 0), Then, which one of the following is correct?a)Rank of T > Nullity of Tb)Nullity of T > Rank of Tc)Rank of T = Nullity of T = 3d)Rank of T = Nullity of T = 2Correct 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 Consider, the linear transformationT : R4 ---->R4 given by:T(x, y, z, u) = (x, y, 0, 0), Then, which one of the following is correct?a)Rank of T > Nullity of Tb)Nullity of T > Rank of Tc)Rank of T = Nullity of T = 3d)Rank of T = Nullity of T = 2Correct answer is option 'D'. Can you explain this answer?.
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