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

User EcologyTom
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1 Answer

5 votes

Answer:

x = -1223, y = -629, and z = -31.

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!!!

User Eric Grunzke
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5.2k points