We have to solve the following system of equations using the Gauss-Jordon elimination method.

2X1 + 6X2 - 32X3 = 26 ...(1)

4X1 + 3X2 - 19X3 = 7 ...(2)

X1 + X2 - 6X3 = 3 ...(3)

There are three variables X1, X2 and X3 and three equations. We get the matrix:

2...6...-32...|...26

4...3...-19...|...7

1...1...-6.....|...3

Divide the first row by 2

1...3...-16...|...13

4...3...-19...|...7

1...1...-6.....|...3

Subtract 4 times row 1 from row 2

1....3...-16...|...13

0...-9....45...|...-45

1...1...-6.....|...3

Subtract row 1 from row 3

1....3...-16...|...13

0...-9....45...|...-45

0...-2...10....|...-10

Divide row 2 by -9

1....3...-16...|...13

0....1....-5....|...-5

0...-2...10....|...-10

Adding 2 times row 2 to row 3 we find that the third row has all zero terms. This shows that the system of equations is dependent.

The system of equations is dependent and therefore there is no unique solution.