Gauss- Elimination Method. t is another method used to solve linear equation

2. Systems of linear equations that must be solved
simultaneously arise in problems that include several
(possibly many) variables that are dependent on each
other.

4. In direct methods, the solution is calculated by
performing arithmetic operations with the equations. In
iterative methods, an initial approximate solution is
assumed and then used in an iterative process for
obtaining successively more accurate solutions.

5. Three (3) direct methods for solving systems of
equations are: Gauss Elimination, Gauss-Jordan, and
LU Decomposition.
Two (2) indirect or iterative methods are: Jacobi and
Gauss-Seidel.

9. In this procedure, a system of equations that is given in
a general form is manipulated to be in upper triangular
form, which is then solved by using back substitution.

11. What is a pivot element?
• element on the left-hand side of a
matrix that you want the elements
above and below to be zero
• first nonzero entry of each row
What is a pivot row?
• the row that contains your pivot
element

15. STEP-BY-STEP
1. Solve for the multiplier,
m =
𝑒𝑙𝑒𝑚𝑒𝑛𝑡 𝑦𝑜𝑢 𝑤𝑎𝑛𝑡 𝑡𝑜 𝑒𝑙𝑖𝑚𝑖𝑛𝑎𝑡𝑒
𝑝𝑖𝑣𝑜𝑡 𝑒𝑙𝑒𝑚𝑒𝑛𝑡
2. Multiply m to the pivot row
3. Subtract the product from the row
you are inspecting

30. 1. The pivot element is zero.

31. 2. The pivot element is small relative to the other terms
in the pivot row.

32. 2. The pivot element is small relative to the other terms
in the pivot row.

33. 2. The pivot element is small relative to the other terms
in the pivot row.

34. 2. The pivot element is small relative to the other terms
in the pivot row.
The numerical calculations are less prone to error and
will have fewer round-off errors if the pivot element has
a larger numerical absolute value compared to the other
elements in the same row.