Answer:
a. x +8z = -1
b. y +5z = 2
c. 0 = 0
d. (x, y, z) = (-1-8z, 2-5z, z)
Step-by-step explanation:
As with the original matrix, the first three columns are the coefficients of the respective variables, and the last column is the constant on the right of the equal sign.
a. The first row represents the equation ...
x + 8z = -1
__
b. The second row represents the equation ...
y + 5z = 2
__
c. The third row represents the equation ...
0 = 0
This equation expresses a truth, so indicates the original system of equations was consistent, but dependent. (a third row of 0 0 0 1 would indicate inconsistent, no solution)
__
d. The system is consistent but dependent. The solution can be written as ...
(x, y, z) = (-1-8z, 2-5z, z) . . . . where z is a free variable
