Question

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.

Answer 1

Answer:

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