Solve the system by the Gauss-Jordan method.
B)
C)
D)
E) inconsistent

Question

Solve the system by the Gauss-Jordan method. ​  ​
B) ​ 
C) ​ 
D) ​ 
E) inconsistent

Quizplus · Accepted Answer

Using the Gauss-Jordan method, we can reduce the augmented matrix to row echelon form and then to reduced row echelon form:

1 2 3 4 | 5 
0 1 2 3 | 4 
0 0 0 -1 | -2

From the last row, we see that 0x + 0y + 0z - w = -2, or w = 2. Back-substituting into the second row, we get 0x + 0y + 2z - 2 = 4, or z = 3. Back-substituting again into the first row, we get x + 2y + 3z - 4 = 5, or x + 2y + 9 = 5, or x + 2y = -4. So the solution is x = -4 - 2y, y is a free variable, z = 3, and w = 2. Therefore, the correct answer is C.

Solve the System by the Gauss-Jordan Method