A consistent homogeneous system has fewer independent equations than unknowns. What can be concluded about its solutions?
Correct answer: C. It has infinitely many solutions
- A. It has only the zero solution
- B. It has no solution
- C. It has infinitely many solutions
- D. It always has exactly two solutions
Explanation
A homogeneous system is always consistent because the zero vector is a solution. When the rank is less than the number of unknowns, at least one free variable exists, producing infinitely many solutions.
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