Solve Equations 2.04x1-x2=48.8;-x1+2.04x2-x3=0.8;-x2+2.04x3=0.8 using Thomas algorithm method

Solution:
Solving tridiagonal matrix system of equations using Thomas algorithm method
Total Equations are `3`

`2.04x1-x2+0x3=48.8 -> (1)`

`-x1+2.04x2-x3=0.8 -> (2)`

`0x1-x2+2.04x3=0.8 -> (3)`

Converting given equations into matrix form

	`2.04`	`-1`	`0`		`48.8`
	`-1`	`2.04`	`-1`		`0.8`
	`0`	`-1`	`2.04`		`0.8`

Identify each number above with Thomas algorithm notation

	`b_1`	`c_1`	`0`		`d_1`
	`a_2`	`b_2`	`c_2`		`d_2`
	`0`	`a_3`	`b_3`		`d_3`

Sub diagonal values are
`a_2=-1,a_3=-1`

Main diagonal values are
`b_1=2.04,b_2=2.04,b_3=2.04`

Super diagonal values are
`c_1=-1,c_2=-1`

Right-hand side values are
`d_1=48.8,d_2=0.8,d_3=0.8`

Step-1 :
`y_i=b_i-(a_i * c_(i-1))/(y_(i-1)), i=2,3`

`y_1=b_1``=2.04`

`y_2=b_2-(a_2 * c_1)/(y_1)`

`=2.04-(-1 * -1)/(2.04)`

`=2.04-0.4902`

`=1.5498`

`y_3=b_3-(a_3 * c_2)/(y_2)`

`=2.04-(-1 * -1)/(1.5498)`

`=2.04-0.6452`

`=1.3948`

Step-2 :
`z_i=(d_i-a_i*z_(i-1))/(y_i), i=2,3`

`z_1=d_1/y_1``=48.8/2.04=23.9216`

`z_2=(d_2-a_2*z_1)/(y_2)`

`=(0.8 - (-1) * 23.9216)/(1.5498)`

`=(24.7216)/(1.5498)`

`=15.9514`

`z_3=(d_3-a_3*z_2)/(y_3)`

`=(0.8 - (-1) * 15.9514)/(1.3948)`

`=(16.7514)/(1.3948)`

`=12.0103`

Step-3 :
`x_i=z_i-(c_i*x_(i+1))/(y_i), i=2,1`

`x_3=z_3``=12.0103`

`x_2=z_2-(c_2*x_3)/(y_2)`

`=15.9514-((-1) * 12.0103)/(1.5498)`

`=15.9514+7.7495`

`=23.701`

`x_1=z_1-(c_1*x_2)/(y_1)`

`=23.9216-((-1) * 23.701)/(2.04)`

`=23.9216+11.6181`

`=35.5397`

Solution is
`x_1=35.5397`

`x_2=23.701`

`x_3=12.0103`

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