Let U, V and W be finite dimensional real vec...
Let U, V and W be finite dimensional real vector spaces, T : U → V, S : V → W and P : W → U be linear transformations. If range (ST) = nullspace (P), nullspace (ST) = range (P) and rank (T) = rank (S), then which one of the following is true?
• a)
nullity of T = nullity of S
• b)
dimension of U ≠ dimension of W
• c)
If dimension of V = 3, dimension of U = 4, then P is not identically zero
• d)
If dimension of V = 4, dimension of U = 3 and T is one- one, then P is identically zero
 1 Crore+ students have signed up on EduRev. Have you?
1 Crore+ students have signed up on EduRev. Have you?

### Learn this topic in detail Math - 2018 Past Year Paper 60 Ques | 180 Mins View courses related to this question

### Quick links for IIT JAM exam 850+
Video Lectures 2500+
Revision Notes 600+
Online Tests 10,000+
Doubts Solved
Let U, V and W be finite dimensional real vector spaces, T : U → V, S : V → W and P : W → U be linear transformations. If range (ST) = nullspace (P), nullspace (ST) = range (P) and rank (T) = rank (S), then which one of the following is true?a)nullity of T = nullity of Sb)dimension of U ≠ dimension of Wc)If dimension of V = 3, dimension of U = 4, then P is not identically zerod)If dimension of V = 4, dimension of U = 3 and T is one- one, then P is identically zeroCorrect answer is option 'C'. Can you explain this answer?
Question Description
Let U, V and W be finite dimensional real vector spaces, T : U → V, S : V → W and P : W → U be linear transformations. If range (ST) = nullspace (P), nullspace (ST) = range (P) and rank (T) = rank (S), then which one of the following is true?a)nullity of T = nullity of Sb)dimension of U ≠ dimension of Wc)If dimension of V = 3, dimension of U = 4, then P is not identically zerod)If dimension of V = 4, dimension of U = 3 and T is one- one, then P is identically zeroCorrect answer is option 'C'. Can you explain this answer? for IIT JAM 2023 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Let U, V and W be finite dimensional real vector spaces, T : U → V, S : V → W and P : W → U be linear transformations. If range (ST) = nullspace (P), nullspace (ST) = range (P) and rank (T) = rank (S), then which one of the following is true?a)nullity of T = nullity of Sb)dimension of U ≠ dimension of Wc)If dimension of V = 3, dimension of U = 4, then P is not identically zerod)If dimension of V = 4, dimension of U = 3 and T is one- one, then P is identically zeroCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for IIT JAM 2023 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let U, V and W be finite dimensional real vector spaces, T : U → V, S : V → W and P : W → U be linear transformations. If range (ST) = nullspace (P), nullspace (ST) = range (P) and rank (T) = rank (S), then which one of the following is true?a)nullity of T = nullity of Sb)dimension of U ≠ dimension of Wc)If dimension of V = 3, dimension of U = 4, then P is not identically zerod)If dimension of V = 4, dimension of U = 3 and T is one- one, then P is identically zeroCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Let U, V and W be finite dimensional real vector spaces, T : U → V, S : V → W and P : W → U be linear transformations. If range (ST) = nullspace (P), nullspace (ST) = range (P) and rank (T) = rank (S), then which one of the following is true?a)nullity of T = nullity of Sb)dimension of U ≠ dimension of Wc)If dimension of V = 3, dimension of U = 4, then P is not identically zerod)If dimension of V = 4, dimension of U = 3 and T is one- one, then P is identically zeroCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for IIT JAM. Download more important topics, notes, lectures and mock test series for IIT JAM Exam by signing up for free.
Here you can find the meaning of Let U, V and W be finite dimensional real vector spaces, T : U → V, S : V → W and P : W → U be linear transformations. If range (ST) = nullspace (P), nullspace (ST) = range (P) and rank (T) = rank (S), then which one of the following is true?a)nullity of T = nullity of Sb)dimension of U ≠ dimension of Wc)If dimension of V = 3, dimension of U = 4, then P is not identically zerod)If dimension of V = 4, dimension of U = 3 and T is one- one, then P is identically zeroCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Let U, V and W be finite dimensional real vector spaces, T : U → V, S : V → W and P : W → U be linear transformations. If range (ST) = nullspace (P), nullspace (ST) = range (P) and rank (T) = rank (S), then which one of the following is true?a)nullity of T = nullity of Sb)dimension of U ≠ dimension of Wc)If dimension of V = 3, dimension of U = 4, then P is not identically zerod)If dimension of V = 4, dimension of U = 3 and T is one- one, then P is identically zeroCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for Let U, V and W be finite dimensional real vector spaces, T : U → V, S : V → W and P : W → U be linear transformations. If range (ST) = nullspace (P), nullspace (ST) = range (P) and rank (T) = rank (S), then which one of the following is true?a)nullity of T = nullity of Sb)dimension of U ≠ dimension of Wc)If dimension of V = 3, dimension of U = 4, then P is not identically zerod)If dimension of V = 4, dimension of U = 3 and T is one- one, then P is identically zeroCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of Let U, V and W be finite dimensional real vector spaces, T : U → V, S : V → W and P : W → U be linear transformations. If range (ST) = nullspace (P), nullspace (ST) = range (P) and rank (T) = rank (S), then which one of the following is true?a)nullity of T = nullity of Sb)dimension of U ≠ dimension of Wc)If dimension of V = 3, dimension of U = 4, then P is not identically zerod)If dimension of V = 4, dimension of U = 3 and T is one- one, then P is identically zeroCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Let U, V and W be finite dimensional real vector spaces, T : U → V, S : V → W and P : W → U be linear transformations. If range (ST) = nullspace (P), nullspace (ST) = range (P) and rank (T) = rank (S), then which one of the following is true?a)nullity of T = nullity of Sb)dimension of U ≠ dimension of Wc)If dimension of V = 3, dimension of U = 4, then P is not identically zerod)If dimension of V = 4, dimension of U = 3 and T is one- one, then P is identically zeroCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice IIT JAM tests. (Scan QR code)