Question

In the matrix equation Px = q, which of the following is necessary condition for the existence of at least one solution for the unknow vector x.

• A. Augmented matrix [P:q] must have the same rank as matrix P
• B. Vector q must have only non-zero elements
• C. Matrix P must be singular
• D. Matrix P must be square

Answer 1

The correct option is A Augmented matrix [P:q] must have the same rank as matrix P

The matrix equation Px = q will have a unique solution in rank (P) = rank [P:q] = n where n, is order of matrix p & sytem will have infinite many solutions in rank (P) = rank [P:q] < n