6.1.1. Direct Methods

Try these first

1. 1.

   Define Gaussian elimination.

   Hint

   What type of matrix form does this technique achieve?

2. 2.

   What is back-substitution?

   Hint

   Think about its order of operations in solving.

3. 3.

   What is the main advantage of Gaussian elimination?

   • It is fast for large systems
   • It is systematic for small to medium systems
   • It requires no computations

   Hint

   Think about its structure and how it helps in solving.

4. 4.

   Gauss-Jordan method results in what type of matrix?

   • Upper triangular
   • Diagonal
   • Identity

   Hint

   What is the final form associated with Gauss-Jordan?

5. 5.

   What happens if you use Gaussian elimination on a singular matrix?

   Hint

   What characteristic defines a singular matrix?

6. 6.

   Design a model using both Gaussian and LU decomposition to solve a practical application in engineering.

   Hint

   What type of engineering problems typically involve large systems?