Question

in each part, the augmented matrix for a linear system is given in which the asterisk represents an unspecified real number. Determine whether the system is consistent, and if so whether the solution is unique. Answer "inconclusive" if there is not enough information to make a decision.

Answer 1

To determine whether a system of linear equations is consistent and whether the solution is unique, we need to analyze the augmented matrix.

Step-by-step explanation:

To determine whether a system of linear equations is consistent and whether the solution is unique, we need to analyze the augmented matrix. If we end up with a coefficient matrix that has a row of zeros followed by a non-zero constant in the last column, the system is inconsistent. If there are no zero rows but there are more unknowns than equations, the system has infinitely many solutions. If there are no zero rows and the number of unknowns is equal to the number of equations, the system has a unique solution.

In summary, we need to examine the augmented matrix closely to determine the consistency and uniqueness of the system.