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f T = |  eigen values of B are in Z}, then which of the following statement(s) is true?
Let T = {B ∈ M3 x 3(ℝ) | eigenvalues of B are integers}. Which of the following statements is/are true?
  • a)
     If B-1 exist for B∈ T, then B-1 ∈ T
  • b)
    There exists B ∈ M3 x 3(ℝ) \ T such that B-1 ∈ T.
  • c)
    If B ∈ T, then B ∈ M3 x 3(ℤ).
  • d)
    If B ∈ M3 x 3(ℚc), then B ∉ T
Correct answer is option 'B'. Can you explain this answer?
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f T = |eigen values of B are in Z}, then which of the following state...
  • For statement A, if B is invertible and its eigenvalues are integers, B-1's eigenvalues are the reciprocals of B's eigenvalues. These may not be integers, contradicting the condition for B-1 to be in T.
  • Statement B is true. An example is B = I, the identity matrix, which is in M3 x 3(ℝ). Here, B-1 = B, and both have integer eigenvalues.
  • Statement C is false because a matrix in T can have integer eigenvalues without having all integer entries.
  • Statement D is false. A matrix can be in M3 x 3(ℚc) and still have integer eigenvalues.
 
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f T = |eigen values of B are in Z}, then which of the following statement(s) is true?Let T = {B ∈ M3 x 3() | eigenvalues of B are integers}. Which of the following statements is/are true?a)If B-1exist forB∈ T, then B-1∈Tb)There exists B ∈ M3 x 3() \ T such that B-1∈ T.c)If B ∈ T, then B ∈ M3 x 3().d)If B ∈ M3 x 3(c), then B ∉ TCorrect 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 f T = |eigen values of B are in Z}, then which of the following statement(s) is true?Let T = {B ∈ M3 x 3() | eigenvalues of B are integers}. Which of the following statements is/are true?a)If B-1exist forB∈ T, then B-1∈Tb)There exists B ∈ M3 x 3() \ T such that B-1∈ T.c)If B ∈ T, then B ∈ M3 x 3().d)If B ∈ M3 x 3(c), then B ∉ TCorrect 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 f T = |eigen values of B are in Z}, then which of the following statement(s) is true?Let T = {B ∈ M3 x 3() | eigenvalues of B are integers}. Which of the following statements is/are true?a)If B-1exist forB∈ T, then B-1∈Tb)There exists B ∈ M3 x 3() \ T such that B-1∈ T.c)If B ∈ T, then B ∈ M3 x 3().d)If B ∈ M3 x 3(c), then B ∉ TCorrect answer is option 'B'. Can you explain this answer?.
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