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!!!

3,000,540

step-by-step explanation: