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In the matrix equation Px = q, which of the following is a necessary condition for the existence of at least one solution for the unknown vector x?
  • a)
    Matrix P must be square.
  • b)
    Vector q must have only non-zero element.
  • c)
    Matrix P must be singular.
  • d)
    Augmented matrix [P q] must have the same rank as matrix P.
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
In the matrix equation Px = q, which of the following is a necessary c...
According to Rouche's theorem, the system is consistent if and only if the co-efficient matrix and the augmented matrix are of the same rank, otherwise the system is inconsistent.
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In the matrix equation Px = q, which of the following is a necessary condition for the existence of at least one solution for the unknown vector x?a)Matrix P must be square.b)Vector q must have only non-zero element.c)Matrix P must be singular.d)Augmented matrix [P q] must have the same rank as matrix P.Correct answer is option 'D'. Can you explain this answer?
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