Thomas Algorithm for solving an equation set with a banded matrix

$0$ solutions submitted $($max: $3)$

There are four spring serially connected. The force$-$balance equations for these spring system are given below:

$k_2(x_2-x_1)=k_1{x}_1$

$k_3(x_3-x_2)=k_2(x_2-x_1)$

$k_4(x_4-x_3)=k_3(x_3-x_2)$

$F=k_4(x_4-x_3)$

where $k_1,k_2,k_3,k_4$ are the spring constants of four springs which are $150,50,80,200k\frac{g}{s^2},$ respectively.

$F=14700N$ is the force applied on the springs.

Calculate $x$ values by solving these equations using the Thomas Algorithm.

For this purpose, first modify the equations such that you have a tridiagonal matrix system $($you can do this by hand $-$ no need to show your hand calculations$).$

Enter the tridiagonal system you obtained into MATLAB as a matrix of $"$A$"$ for coefficients of unknowns and a vector of $"$b$"$ for constants on the right hand side.

A matrix should be $44$ tridiagonal matrix, b vector should be $14$ matrix such as $b=[b1,b2,b3,b4]$

Then, write a script which accepts inputs of A and $b$ for the Thomas Algorithm steps of a$)$ Decomposition b$)$ Forward substutition c$)$ Back Substutition.

Use "while" loop for the loops of these steps

The outputs should be in a $1$ x $4$ vector defined as $"$x$"$ vector in MATLAB such as $x=[x1,x2,x3,x4].$

Do NOT use backslash operator or any other MATLAB solver functions to compute the output.

A simple test case has been provided to test your solution before submitting.$|$ b $=[]$;

x $=$ thomasal$($A$,$b$)$

$\%$ Thomas algorithm

function x $=$ thomasal$($A$,$b$)$

$\%$ Initialize the output vector.

n $=$ length$($b$)$;

$\%$ Do the three steps of Thomas algorithm below.

$\%$ a$)$ Decomposition

while

end

$\%$ b$)$ Forward substitution

while

end

$\%$ c$)$ Back substitution

while

end

end $\%$ end of function Assessment:

Is the input b vector correct $?($It should be a $14$ matrix.$)($Pretest$)$

Is the input A matrix correct?

Is the output calculated by Thomas algorithm correct?

Was backslash used to compute the results?

Does the code involve while loop?There are four spring serially connected. The force$-$balance equations for these spring system are given below:

where are the spring constants of four springs which are $150,50,80,200,$ respectively.

$=14700$ N is the force applied on the springs.

Calculate x values by solving these equations using the Thomas Algorithm.

For this purpose, first modify the equations such that you have a tridiagonal matrix system $($you can do this by hand $-$ no need to show your hand calculations$).$

Enter the tridiagonal system you obtained into MATLAB as a matrix of $"$A$"$ for coefficients of unknowns and a vector of $"$b$"$ for constants on the right hand side.

A matrix should be $4$x$4$ tridiagonal matrix, b vector should be $1$x$4$ matrix such as b$=[$b$1,$b$2,$b$3,$b$4]$

Then, write a script which accepts inputs of A and b for the Thomas Algorithm steps of a$)$ Decomposition b$)$ Forward substutition c$)$ Back Substutition.

Use "while" loop for the loops of these steps

The outputs should be in a $1$x$4$ vector defined as $"$x$"$ vector in MATLAB such as x$=[$x$1,$x$2,$x$3,$x$4].$

Do NOT use backslash operator or any other MATLAB solver functions to compute the output.

A simple test case has been provided to test your solution before submitting.