Solve the following problems by hand. When needed, use a calculator or write a MATLAB script file to carry out calculations Given the following set of equations

4*x12*x2x3 = 3

x16*x2+2*x3 = 5

x13*x2+12*x3 = 31

solve by hand using 1. Gaussian elimination (partial pivoting), 2. LU Decomposition, 3. Matrix Inverse.

Problems to be solved using MATLAB

Resolve problem given in the section above using

MATLABs left division (x = A\b),

MATLABs inverse operation (x = A1b),

MATLABs built in function for LU decomposition or our own LU decomposition algorithm.

Write a Matlab script that: (i) calls the different methods, (ii) stores the solution obtained with each method in a separate vector and (iii) verifies that all solutions are the same. As usual, comment your script to explain what you are doing.

Hand in your Matlab script together with an output of the execution of your script.