Given that the augmented matrix in row-reduced form below is equivalent to the augmented matrix of a system of linear equations. Determine whether the system has a solution and find the solution (s) to the system, if they exist.

[ 1 0 0 0 | - 9 ]

[ 0 1 1 0 | - 8 ]

[ 0 0 0 1 | 1 ]

A) x=-9, y=-8, z=-8, w=1

B) No solution.

C) x=-9, y=-8, z=1

D) x=-9, y=-8+z, w=1, z=any real number

E) z=-9, y=-8-z, w=1, z=any real number

F) None of the above.

x=9, y = -8-z, w = 1, z=z

Step-by-step explanation:

Given that the augmented matrix in row-reduced form below is equivalent to the augmented matrix of a system of linear equations.

[ 1 0 0 0 | - 9 ]

[ 0 1 1 0 | - 8 ]

[ 0 0 0 1 | 1 ]

We find that this is a rectangular matrix 3 rows and 4 columns

i. e. the variarables are four but independent equations are only 3.

so only parametric equations can be found out

First row gives x = - 9

Last row gives w = 1

II row gives y+z = -8 and we do not have any other equation in y or z

Hence we have solutoin as

z = z and y - 8-z

The solution set is

x=9, y = -8-z, w = 1, z=z