GATE | GATE CS 1996 | Question 7

Let Ax=b be a system of linear equations where A is an m×n matrix and b is a m×1 column vector and X is an n×1 column vector of unknowns. Which of the following is false?
(A) The system has a solution if and only if, both A and the augmented matrix [Ab] have the same rank
(B) If m<n and b is the zero vector, then the system has infinitely many solutions
(C) If m=n and b is a non-zero vector, then the system has a unique solution
(D) The system will have only a trivial solution when m=n, b is the zero vector and rank(A) = n

Answer: (C)


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