Question

Solve the following systems of equations using Gauss-Jordan row reduction, i.e., solve via writing the augmented matrix in reduced row echelon form. 3x₂ + 6x₃ = 9 -x₁ + x₂ - 2x₃ = -1

Answer 1

The given system of equations, when processed with Gauss-Jordan reduction, reveals a contradiction. Therefore, there is no solution to the system.

Step-by-step explanation:

To solve the given system of equations using Gauss-Jordan reduction, we begin by forming an augmented matrix. The system 3x₂ + 6x₃ = 9 and -x₁ + x₂ - 2x₃ = -1 becomes the augmented matrix:

[0 3 6 | 9]
[-1 1 -2 | -1].

We can start the row operations to reduce this matrix. As the first element in the first row is zero, we want to swap the rows:

[-1 1 -2 | -1]
[0 3 6 | 9].

Next, we'll make the first element of the first row 1 by multiplying the row by -1:

[1 -1 2 | 1]
[0 3 6 | 9].

Our next step is to make the second element in the first row 0 by adding three times the first row to the second row:

[1 -1 2 | 1]
[0 0 0 | 12].

However, as the second row implies '0 = 12', we have a contradiction, which indicates that the given system of equations has no solution.

Learn more about Gauss-Jordan Elimination