Use row reduction to solve the system of equations. x-2y+z=4, 3x-5y-17z=3, 2x-6y+43z=-5

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!