Person A: Hey, have you figured out the solution to the system of equations?
Person B: Yes, I managed to solve it using the Gauss-Elimination method. It involved breaking down the matrix and manipulating it step by step.
Person A: That sounds complicated. How did you go about it?
Person B: Well, first I started by eliminating the coefficients below the first entry in the first column. It means getting rid of the numbers below the 3 in the first row.
Person A: Ah, I see. So, what did you do next?
Person B: After that, I proceeded to eliminate the coefficient below the second entry in the second column. That involved removing the number below the -11/3 in the second row.
Person A: And then, did you obtain the values for the variables?
Person B: Yes, but not directly. After reducing the matrix to row-echelon form, I performed back-substitution to find the values of x, y, and z.
Person A: That's impressive! So, what were the final solutions?
Person B: Well, the values I obtained were x = 17/8, y = 173/176, and z = 17/16. It took a bit of work, but I managed to solve it.
Phrasal verbs used in the dialogue:
1. Figure out - Meaning: To solve or understand something.
2. Break down - Meaning: To separate or divide into smaller parts.
3. Manipulate - Meaning: To handle or control skillfully.
4. Get rid of - Meaning: To eliminate or remove something.
5. Perform - Meaning: To carry out or execute a task or action.
Step-by-step explanation: