The question asks which of the listed actions is NOT allowed when performing Gaussian elimination.

Here are the valid operations in Gaussian elimination:

1. Interchanging (swapping) two rows – This is allowed.
2. Multiplying a row by a non-zero constant – This is allowed.
3. Adding a multiple of one row to another row – This is allowed.

Now, examining the options:

• Interchanging two rows: Allowed.
• Multiplying a row by a non-zero constant: Allowed.
• Adding a constant to a row: NOT allowed.
• Adding values from one row to another row: Allowed.

Thus, the correct answer is: Adding a constant to a row in a matrix is not an allowed action in Gaussian elimination.

Would you like any more details or have other questions?

Here are 5 related questions to expand your understanding:

1. What is the purpose of Gaussian elimination in solving linear systems?
2. How does row echelon form differ from reduced row echelon form?
3. Why is it important that only non-zero constants are allowed for row multiplication in Gaussian elimination?
4. Can you describe the process of back substitution in Gaussian elimination?
5. What are some applications of Gaussian elimination outside of solving systems of equations?

Tip: When performing Gaussian elimination, always focus on transforming the matrix step by step into row echelon form while maintaining the allowed operations.