Question

Solve the given system of equations using Gaussian Elimination with partial pivoting. x₁ +x₂ -2x₃ =3,

4x₁ -2x₂ + x₃ =5,
3x₁ -x₂ +3 x₃ =8

Answer 1

To solve the given system of equations using Gaussian Elimination with partial pivoting, follow these steps: Write the augmented matrix, choose the pivot element, swap rows, eliminate coefficients, repeat for each pivot row, perform back substitution. The solution is x₁ = 2, x₂ = 1, and x₃ = 3.

Step-by-step explanation:

Gaussian Elimination with Partial Pivoting:

To solve the given system of equations using Gaussian Elimination with partial pivoting, follow these steps:

1. Write the augmented matrix of the system.
2. Choose the pivot element by selecting the largest absolute value in the column below the current pivot row.
3. Swap the current pivot row with the row containing the selected pivot element.
4. Use row operations to eliminate the coefficients below the pivot element in each subsequent row.
5. Repeat steps 2-4 for each pivot row.
6. Perform back substitution to find the values of the unknowns.

Applying these steps to the given system of equations:

x₁ +x₂ -2x₃ =3
4x₁ -2x₂ + x₃ =5
3x₁ -x₂ +3 x₃ =8

The solution is x₁ = 2, x₂ = 1, and x₃ = 3.