Answer:
x = -1223, y = -629, and z = -31.
Step-by-step 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:
• 1 -2 1 | 4
• 3 -5 -17 | 3
• 2 -6 43 | -5
Step 2: Multiply row 1 with -3 and add it in row 2:
• 1 -2 1 | 4
• 0 1 -20 | -9
• 2 -6 43 | -5
Step 3: Multiply row 1 with -2 and add it in row 3:
• 1 -2 1 | 4
• 0 1 -20 | -9
• 0 -2 41 | -13
Step 4: Multiply row 2 with 2 and add it in row 3:
0 2 -40 -18
• 1 -2 1 | 4
• 0 1 -20 | -9
• 0 0 1 | -31
Step 5: It can be seen that when this updated augmented matrix is converted into a system, it comes out to be:
• x - 2y + z = 4
• y - 20z = -9
• z = -31
Step 6: Since we have calculated z = -31, put this value in equation 2:
• y - 20(-31) = -9
• y = -9 - 620
• y = -629.
Step 8: Put z = -31 and y = -629 in equation 1:
• x - 2(-629) - 31 = 4
• x + 1258 - 31 = 4
• x = 35 - 1258.
• x = -1223
So final answer is x = -1223, y = -629, and z = -31!!!
