Let Ax = b be a system of linear equations where A is an m x n matrix, b is an…
GATE · 1996 · CS · Question 1 subparts
Let Ax = b be a system of linear equations where A is an m x n matrix, b is an m x 1 column vector, and x is an n x 1 column vector of unknowns. Which of the following is false?
- A.
The system has a solution if and only if A and the augmented matrix [A b] 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
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