The number of 3 x 3 matrices A whose entries are either 0 or 1 and for which the system A[x y z]^T = [1 0 0]^T has exactly two distinct solutions is:
Step-by-Step Solution
Key Concept: A system of linear equations Ax = b has either zero, one, or infinitely many solutions. It can never have exactly two distinct solutions.
A system of linear equations Ax = b can have either a unique solution, no solution, or infinitely many solutions. It is impossible for a system of linear equations to have exactly two distinct solutions. Therefore, the number of such matrices is 0.
Correct Answer: 1