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® EX use G.E method to Solve the following system of + ox, +882 2x3 3x + 582 + 2x₂ 6x + 2x2 + 8X₃ -7 8 26 © AX - b au O 8 2 7 Bazz 2 x X2 X₂ 3 6 8 8 26 933 3 5 8 ES O 2 -7 Xi X2 X2 8 2 6 8 26

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Answer:

To solve the given system of equations using the Gaussian Elimination method, we'll first write down the augmented matrix and then perform row operations to simplify it.

The given system of equations is:

1x + 1x₂ + 882x₃ = 582 (Equation 1)

2x + 6x₂ + 2x₂ + 8x₃ = -7 (Equation 2)

8x + 2x₂ + 6x₃ = 26 (Equation 3)

We can represent this system as an augmented matrix [A|b]:

[ 1 1 882 | 582 ]

[ 2 6 2 | -7 ]

[ 8 2 6 | 26 ]

Now, we'll perform row operations to simplify the augmented matrix:

R2 = R2 - 2R1

R3 = R3 - 8R1

The updated matrix becomes:

[ 1 1 882 | 582 ]

[ 0 4 -1762 | -1171 ]

[ 0 -6 -6976 | -4562 ]

Next, we'll perform additional row operations to further simplify the matrix:

R2 = R2/4

R3 = R3 + 1.5R2

The updated matrix becomes:

[ 1 1 882 | 582 ]

[ 0 1 -441 | -292.75 ]

[ 0 0 -11132 | -7610.625 ]

Finally, we'll perform the last row operation:

R3 = R3/(-11132)

The final matrix becomes:

[ 1 1 882 | 582 ]

[ 0 1 -441 | -292.75 ]

[ 0 0 1 | 0.68475 ]

Now, we'll work our way back up, starting from the bottom row, to find the values of the variables:

From the third row, we can determine that x₃ = 0.68475.

Substituting this value back into the second row, we can solve for x₂:

1x + 1(-441) + 882(0.68475) = 582

x - 441 + 604.05 = 582

x - 441 = -22.05

x = -22.05 + 441

x = 418.95

Finally, substituting the values of x₃ = 0.68475 and x₂ = 418.95 into the first row, we can solve for x:

1(418.95) + 1(-441) + 882(0.68475) = 582

418.95 - 441 + 604.05 = 582

582 = 582

Therefore, the solution to the given system of equations is:

x = 418.95

x₂ = -441

x₃ = 0.68475

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