Answer:
Option D (x = 1, y = -2, and z = 7).
Explanation:
This question can be solved using multiple ways. I will use the Gauss Jordan Method.
Step 1: Convert the system into the augmented matrix form:
• 0 -4 0 | 8
• 1 3 -3 | -26
• 2 -5 1 | 19
Step 2: Divide row 1 by -4 and switch row 1 and row 2:
• 1 3 -3 | -26
• 0 1 0 | -2
• 2 -5 1 | 19
Step 3: Multiply row 1 with -2 and add it in row 3:
• 1 3 -3 | -26
• 0 1 0 | -2
• 0 -11 7 | 71
Step 4: Multiply row 2 with 11 and add it in row 3:
• 1 3 -3 | -26
• 0 1 0 | -2
• 0 0 7 | 49
Step 5: Divide row 3 with 7:
• 1 3 -3 | -26
• 0 1 0 | -2
• 0 0 1 | 7
Step 6: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:
• x + 3y - 3z = -26
• y = -2
• z = 7
Step 7: Put z = 7 and y = -2 in equation 1:
• x + 3(-2) - 3(7) = -26
• x - 6 - 21 = -26
• x = 1.
So final answer is x = 1, y = -2, and z = 7. Therefore, Option D is the correct answer!!!