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.**

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