Question

Gauss Elimination Back Substitution. Solving systems of linear equations using Gauss Elimination Back Substitution method.

2y−z=13
x−3y+z=8
x−3y−3z=−4

a) x=2,y=3,z=4
b) x=1,y=−2,z=3
c) x=−1,y=4,z=−5
d) x=0,y=1,z=−2

Answer 1

Gauss Elimination Back Substitution is a method used to solve systems of linear equations. The given system can be solved using this method by following these steps: write the equations in matrix form, perform row operations, and then perform back substitution. The correct answer is d) x=0, y=1, z=−2.

Step-by-step explanation:

Gauss Elimination Back Substitution is a method used to solve systems of linear equations. The given system of equations:
2y − z = 13
x − 3y + z = 8
x − 3y − 3z = −4
can be solved using this method. Here are the steps:

1. Write the system of equations in matrix form.
2. Perform row operations to transform the matrix into row-echelon form.
3. Perform back substitution to find the values of the variables.

The correct answer is d) x=0, y=1, z=−2.