Question

In the homogeneous system with three unknowns, $\rho \left(A\right)=$ number of unknowns, then the system has

• A. Only trivial solution
• B. Reduces to $2$ equations and has infinitely many solutions
• C. Reduces to a single equation and has finitely many solutions
• D. Is inconsistent

Answer 1

The correct option is A Only trivial solution

Since the rank of the matrix is equal to the number of unknowns, the system of equations is consistent and has a unique solution.

Since the system of equations is homogeneous, it only has trivial solution.