Solving systems of linear equations using Gauss Jacobi method calculator

SolutionHelp

$2x+y+z=5,3x+5y+2z=15,2x+y+4z=8$

$2x+5y=16,3x+y=11$

$2x+5y=21,x+2y=8$

$2x+y=8,x+2y=1$

$2x+3y-z=5,3x+2y+z=10,x-5y+3z=0$

$x+y+z=3,2x-y-z=3,x-y+z=9$

$x+y+z=7,x+2y+2z=13,x+3y+z=13$

$2x-y+3z=1,-3x+4y-5z=0,x+3y-6z=0$

Example

1. Solve Equations 2x+5y=21,x+2y=8 using Gauss Jacobi method

Solution:
Total Equations are

$2$

$2x+5y=21$

$x+2y=8$

From the above equations

$x_(k+1)=1/2(21-5y_(k))$

$y_(k+1)=1/2(8-x_(k))$

Initial gauss

$(x,y) = (0,0)$

Solution steps are

$1^(st)$ Approximation

$x_1=1/2[21-5(0)]=1/2[21]=10.5$

$y_1=1/2[8-(0)]=1/2[8]=4$

$2^(nd)$ Approximation

$x_2=1/2[21-5(4)]=1/2[1]=0.5$

$y_2=1/2[8-(10.5)]=1/2[-2.5]=-1.25$

$3^(rd)$ Approximation

$x_3=1/2[21-5(-1.25)]=1/2[27.25]=13.625$

$y_3=1/2[8-(0.5)]=1/2[7.5]=3.75$

$4^(th)$ Approximation

$x_4=1/2[21-5(3.75)]=1/2[2.25]=1.125$

$y_4=1/2[8-(13.625)]=1/2[-5.625]=-2.8125$

$5^(th)$ Approximation

$x_5=1/2[21-5(-2.8125)]=1/2[35.0625]=17.5312$

$y_5=1/2[8-(1.125)]=1/2[6.875]=3.4375$

$6^(th)$ Approximation

$x_6=1/2[21-5(3.4375)]=1/2[3.8125]=1.9062$

$y_6=1/2[8-(17.5312)]=1/2[-9.5312]=-4.7656$

$7^(th)$ Approximation

$x_7=1/2[21-5(-4.7656)]=1/2[44.8281]=22.4141$

$y_7=1/2[8-(1.9062)]=1/2[6.0938]=3.0469$

Equations are Divergent...
Intertions are tabulated as below