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.