Question

3x1−4x2−x3=1

2x1−3x2+x3=1
x1−2x2+3x3=2
solve the system of equations using Gauss-Jordan elimination please use augmented matrices and put them in reduced row-echelon form..

Answer 1

The system of equations is solved using matrix representation, Gauss-Jordan method and the reduced row-echelon form. The solution obtained for the variables are x1=1, x2=1, x3=1.

Step-by-step explanation:

The system of equations given:

3x1−4x2−x3=1
2x1−3x2+x3=1
x1−2x2+3x3=2

First, we form the augmented matrix:

[3 -4 -1 | 1]
[2 -3 1 | 1]
[1 -2 3 | 2]

Next, we use Gaussian elimination to get it into row-echelon form.

[1 -4/3 1/3 | 1/3]
[0 1 -2 | 1]
[0 0 1 | 1]

Then we use Gauss-Jordan elimination to transform the matrix to reduced row-echelon form:

[1 0 0 | 1]
[0 1 0 | 1]
[0 0 1 | 1]

The solution to the system of equations is then x1=1, x2=1, x3=1.

Learn more about Gauss-Jordan Elimination