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Let P be a 3 × 3 non-null real matrix. If there exist a 3 × 2 real matrix Q and a 2 × 3 real matrix R such that P = QR, then
  • a)
    Px = 0 has a unique solution, where 0 ∈ ℝ3
  • b)
    there exists b ∈ ℝ3 such that Px = b has no solution
  • c)
    there exists a non-zero b ∈ ℝ3 such that Px = b has a unique solution
  • d)
    there exists a non-zero b ∈ ℝ3 such that PT x = b has a unique solution
Correct answer is option 'B'. Can you explain this answer?
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Let Pbe a 3 × 3 non-null real matrix. If there exist a 3 ×...
Find the rank of P using the rank formula then its all about LI and LD questions.
RankP = 2 or 1 but not 3

So it will form an LD solution for which Px=b will not have a solution if the b we select e.g. (1, 1, 1), this will not have any solution in echelon form.

Correct answer= b
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Let Pbe a 3 × 3 non-null real matrix. If there exist a 3 × 2 real matrix Qand a 2 × 3 real matrix Rsuch that P= QR, thena) Px= 0 has a unique solution, where 0 ∈ 3b) there exists b∈ 3 such that Px= b has no solutionc) there exists a non-zero b ∈ 3 such that Px= bhas a unique solutiond) there exists a non-zero b ∈ 3 such that PTx = b has a unique solutionCorrect answer is option 'B'. Can you explain this answer?
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Let Pbe a 3 × 3 non-null real matrix. If there exist a 3 × 2 real matrix Qand a 2 × 3 real matrix Rsuch that P= QR, thena) Px= 0 has a unique solution, where 0 ∈ 3b) there exists b∈ 3 such that Px= b has no solutionc) there exists a non-zero b ∈ 3 such that Px= bhas a unique solutiond) there exists a non-zero b ∈ 3 such that PTx = b has a unique solutionCorrect answer is option 'B'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Let Pbe a 3 × 3 non-null real matrix. If there exist a 3 × 2 real matrix Qand a 2 × 3 real matrix Rsuch that P= QR, thena) Px= 0 has a unique solution, where 0 ∈ 3b) there exists b∈ 3 such that Px= b has no solutionc) there exists a non-zero b ∈ 3 such that Px= bhas a unique solutiond) there exists a non-zero b ∈ 3 such that PTx = b has a unique solutionCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let Pbe a 3 × 3 non-null real matrix. If there exist a 3 × 2 real matrix Qand a 2 × 3 real matrix Rsuch that P= QR, thena) Px= 0 has a unique solution, where 0 ∈ 3b) there exists b∈ 3 such that Px= b has no solutionc) there exists a non-zero b ∈ 3 such that Px= bhas a unique solutiond) there exists a non-zero b ∈ 3 such that PTx = b has a unique solutionCorrect answer is option 'B'. Can you explain this answer?.
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