In MATLAB I want to create a code that gets an Augmented matrix (Concatenating A and B) and produce the linear combination of the system in terms of the free variables. The free variables will be given the variables t1, t2, ..., tn for the nth free variables. The inputs and outputs should be matched below. The code should be able to output the linear combination of the system in terms of the free variables regardless of the size of the matrix, for example, a 1 x 10, 5 x 5, or 7 x 3. Look at the 2 test cases below and make sure that the code could output the linear combination as a whole with its column matrices and free variables. PLEASE make sure the program is without error and the inputs are equivalent to the outputs.

Code:

A = [2 3 4 56 6 8;1 2 4 5 6 7;3 6 12 15 18 21;4 6 8 112 12 16]; B = [9;8;24;18]; Aug = [A B] RREF = rref(Aug)

Input:

Output:

x1= 4t1 - 97t2 +6t3 + 5t4 +6t5 x2= -4t1 + 46t2 - 6t3 - 6t4 - 7t5 x3= t1 x4= t2 x5= t3 x6= t4 x7= t5 

Input:

Output:

x1= -4/3t1 - 5/3t2 - 1/3t3 x2= t1 x3= t2

213432664412856515112661812872116982418RREF>100001004400974600660056006700 (31.54252.5121)>(10340350310)