Solve the equation using Gauss Naïve method, a) 3x1 − 2x2 + x3 = −10, 2x1 + 6x2 − 4x3 = −10, −8x1 − 2x2 + 5x3 = −26

Step-by-step explanation:

Given the system of equation

3x1 − 2x2 + x3 = −10 1

2x1 + 6x2 − 4x3 = −10 2

−8x1 − 2x2 + 5x3 = −26   3

Reduce the system of equations:

multiply equation 1 by 3 and add to 2

Eqn 1 * 3 gives;

9x1 − 6x2 + 3x3 = −30

Add to equation 2:

9x1+2x1 +(3x3-4x3) = -30-10

11x1 - x3 = -40 4

multiply eqn 3 by 3 and add to eqn 2

eqn 3 * 3 gives

−24x1 − 6x2 + 15x3 = − 78

Add to eqn 2:

-24x1+2x1)+15x3-4x3 = -78-10

-22x1 + 11x3 = -88 5

solve 4 and 5:

11x1 - x3 = -40 4 * 2

-22x1 + 11x3 = -88 5 * 1

22x1 - 2x3 = -80

-22x1 + 11x3 = -88

Add together:

-2x3 + 11x3 = -80-88

9x3 = -168

x3 = -168/9

x3 = 18.7

subtitute x3 = 18.7 into 4

11x1 - 18.7 = -40

11x1 = -40+18.7

11x1 = -21.3

x1 = -21.3/11

x1 = -1.93

Substitute x1 and x3 into 1

3(-1.93)− 2x2 + 18.7 = −10

- 5.79-2x2 = -28.7

-2x2 = -18.7 +5.79

-2x2 = -22.91

x2 = 11.455

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step-by-step explanation: