Question

The system of linear equations has a unique solution. Find the solution using Gaussian elimination or Gauss-Jordan elimination. {x+y+z =2 {2 x-3 y+2 z =4 {4 x+y-3 z =1

Answer 1

The student can solve the system of linear equations x + y + z = 2, 2x - 3y + 2z = 4, 4x + y - 3z = 1 using Gaussian elimination by forming an upper triangular matrix and then applying back-substitution to find the unique solution.

Step-by-step explanation:

The system of linear equations provided by the student can be solved using Gaussian elimination or Gauss-Jordan elimination. The equations are:

• x + y + z = 2
• 2x - 3y + 2z = 4
• 4x + y - 3z = 1

To solve these equations, we will use Gaussian elimination steps, which involve converting the system of equations into an upper triangular matrix and then performing back-substitution. Below are the steps of Gaussian elimination:

1. Write the augmented matrix of the system.
2. Use row operations to obtain zeros below the pivot in the first column.
3. Move to the next column and repeat the process to form an upper triangular matrix.
4. Perform back-substitution to find the values of x, y, and z.

After following these steps, we would arrive at the unique solution for the given system of equations.