25.10.1. Gaussian Elimination

Try these first

1. 1.

   What is the first step in the Gaussian elimination process?

   Hint

   Think about how we prepare the matrix for substitution.

2. 2.

   List one type of row operation used in Gaussian elimination.

   Hint

   What operations can change the arrangement of matrix rows?

3. 3.

   What is the final step in Gaussian elimination?

   Hint

   What do you do after transforming the matrix into upper triangular form?

4. 4.

   True or False: Gaussian elimination can be used to solve any system of linear equations.

   • True
   • False

   Hint

   Is there a reason it wouldn't apply?

5. 5.

   Solve the following system using Gaussian elimination: \begin{align*} x + 2y + 3z &= 9 \\ 2x + 3y + z &= 8 \\ 3x + y + 2z &= 7 \end{align*}

   Hint

   Modify each equation until zeros are created beneath pivots.

6. 6.

   A matrix represents a system where Gaussian elimination leads to a row of zeros. What conclusions can you draw about the solution's nature?

   Hint

   Investigate if the equations remain true even with one row eliminated.