Solve each system in three variables using Gaussian elimination.

Question

State whether each system is independent, dependent, or inconsistent.
x - y + z = 2
-x + y + z = 4
-x + z = 2

Answer 1

Gaussian Elimination:

The linear equations are x  - y  + z  = 2, - x  + y  + z  = 4 and - x  + z  = 2.

Write the equations into matrix form AX = D .

A  is coefficient matrix , X  is variable matrix and D  is Constant matrix.

The augmented matrix is [AD ]

  are represents first row ,second row and third row .

Solution : x  = 1, y  = 2, z  = 3.

The system of equations has exactly one solution, so the system is consistent and independent.