Q.If $\rho(A) = \rho(A, B) =$ the number of unknowns, then the system is ______.

$\rho(A) = \rho(A,B) =$ number of unknowns is exactly the condition for a unique solution.

For a system $AX = B$ the rank test classifies the solution:

• If $\rho(A) e \rho(A,B)$, the system is inconsistent (no solution).
• If $\rho(A) = \rho(A,B) = n$ (number of unknowns), the system is consistent with a unique solution. …