Mathematics Exam  >  Mathematics Questions  >  In the matrix equation PX = q, which of the f... Start Learning for Free
In the matrix equation PX = q, which of the following is necessary condition for the existence of atleast one solution for the unknown vector
  • a)
    Augmented matrix [P q] must have the same rank as matrix P
  • b)
    Vector q must have only non — zero elemetns
  • c)
    Matrix P must be singular
  • d)
    Matrix P must be square
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In the matrix equation PX = q, which of the following is necessary con...
Free Test
Community Answer
In the matrix equation PX = q, which of the following is necessary con...
Understanding the Matrix Equation PX = q
In the context of the matrix equation PX = q, where P is a matrix, X is the unknown vector, and q is the result vector, it is crucial to determine conditions for the existence of at least one solution.
Necessary Condition for Solutions
- The key condition for this equation to have at least one solution is that the augmented matrix [P q] must have the same rank as the matrix P.
Importance of Rank
- Rank of a Matrix: The rank of a matrix is the maximum number of linearly independent column vectors in the matrix. It indicates the dimension of the column space.
- Augmented Matrix: The augmented matrix [P q] combines the matrix P with the vector q.
- Rank Condition: If the rank of the augmented matrix [P q] is equal to the rank of matrix P, it implies that the system of equations represented by PX = q is consistent, meaning at least one solution exists.
Why Other Options Are Incorrect
- Option B: Vector q must have only non-zero elements.
- This is not a requirement; q can have zero elements and still allow for a solution.
- Option C: Matrix P must be singular.
- A singular matrix may or may not have solutions; it is not a necessary condition.
- Option D: Matrix P must be square.
- P can be rectangular; the condition on ranks is what matters for solutions.
Conclusion
- Hence, the necessary condition for the existence of at least one solution in the equation PX = q is indeed that the ranks of the augmented matrix and matrix P must be equal, confirming that option A is correct.
Explore Courses for Mathematics exam
Question Description
In the matrix equation PX = q, which of the following is necessary condition for the existence of atleast one solution for the unknown vectora)Augmented matrix [P q] must have the same rank as matrix Pb)Vector q must have only non — zero elemetnsc)Matrix P must be singulard)Matrix P must be squareCorrect answer is option 'A'. 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 In the matrix equation PX = q, which of the following is necessary condition for the existence of atleast one solution for the unknown vectora)Augmented matrix [P q] must have the same rank as matrix Pb)Vector q must have only non — zero elemetnsc)Matrix P must be singulard)Matrix P must be squareCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the matrix equation PX = q, which of the following is necessary condition for the existence of atleast one solution for the unknown vectora)Augmented matrix [P q] must have the same rank as matrix Pb)Vector q must have only non — zero elemetnsc)Matrix P must be singulard)Matrix P must be squareCorrect answer is option 'A'. Can you explain this answer?.
Solutions for In the matrix equation PX = q, which of the following is necessary condition for the existence of atleast one solution for the unknown vectora)Augmented matrix [P q] must have the same rank as matrix Pb)Vector q must have only non — zero elemetnsc)Matrix P must be singulard)Matrix P must be squareCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mathematics. Download more important topics, notes, lectures and mock test series for Mathematics Exam by signing up for free.
Here you can find the meaning of In the matrix equation PX = q, which of the following is necessary condition for the existence of atleast one solution for the unknown vectora)Augmented matrix [P q] must have the same rank as matrix Pb)Vector q must have only non — zero elemetnsc)Matrix P must be singulard)Matrix P must be squareCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of In the matrix equation PX = q, which of the following is necessary condition for the existence of atleast one solution for the unknown vectora)Augmented matrix [P q] must have the same rank as matrix Pb)Vector q must have only non — zero elemetnsc)Matrix P must be singulard)Matrix P must be squareCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for In the matrix equation PX = q, which of the following is necessary condition for the existence of atleast one solution for the unknown vectora)Augmented matrix [P q] must have the same rank as matrix Pb)Vector q must have only non — zero elemetnsc)Matrix P must be singulard)Matrix P must be squareCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of In the matrix equation PX = q, which of the following is necessary condition for the existence of atleast one solution for the unknown vectora)Augmented matrix [P q] must have the same rank as matrix Pb)Vector q must have only non — zero elemetnsc)Matrix P must be singulard)Matrix P must be squareCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice In the matrix equation PX = q, which of the following is necessary condition for the existence of atleast one solution for the unknown vectora)Augmented matrix [P q] must have the same rank as matrix Pb)Vector q must have only non — zero elemetnsc)Matrix P must be singulard)Matrix P must be squareCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Mathematics tests.
Explore Courses for Mathematics exam
Signup to solve all Doubts
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev