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Consider a real vector space V of dimension n and a non-zero linear transformationT : V → V. If dimension(T(V)) < nand T2 = λ T, for somethen which of the following statements is TRUE?a)determinant(T) =|λ|nb)There exists a non-trivial subspace V1 of V such that T(X) =0 for all X∈ V1c)T is invertibled)λ is the only eigenvalue of TCorrect answer is option 'B'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider a real vector space V of dimension n and a non-zero linear transformationT : V → V. If dimension(T(V)) < nand T2 = λ T, for somethen which of the following statements is TRUE?a)determinant(T) =|λ|nb)There exists a non-trivial subspace V1 of V such that T(X) =0 for all X∈ V1c)T is invertibled)λ is the only eigenvalue of TCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a real vector space V of dimension n and a non-zero linear transformationT : V → V. If dimension(T(V)) < nand T2 = λ T, for somethen which of the following statements is TRUE?a)determinant(T) =|λ|nb)There exists a non-trivial subspace V1 of V such that T(X) =0 for all X∈ V1c)T is invertibled)λ is the only eigenvalue of TCorrect answer is option 'B'. Can you explain this answer?.

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