Given that the augmented matrix in row-reduced form is equivalent to the augmented matrix of a system of linear equations, determine whether the system has a solution and find the solution or solutions to the system, if they exist.
E) The system is inconsistent

Question

Given that the augmented matrix in row-reduced form is equivalent to the augmented matrix of a system of linear equations, determine whether the system has a solution and find the solution or solutions to the system, if they exist. 
E) The system is inconsistent

Quizplus · Accepted Answer

The last row of the row-reduced augmented matrix is [0 0 1 | -3]. This implies that the equation 0x + 0y + 1z = -3 is part of the system. But this equation clearly has no solution, since there is no value of z that can make the left-hand side equal to -3. Therefore, the system is inconsistent and there is no solution.

Given That the Augmented Matrix in Row-Reduced Form Is Equivalent