The following system of linear equations is called underdetermined because there are more variables than equations. x1+2x23x3=42x1x2+4x3=3 Similarly, the following system is overdetermined because there are more equations than variables. x1+3x2=52x12x2=3x1+7x2=0 You are going to explore whether the number of variables and the number of equations have any bearing on the consistency of a system of linear equations. (a) For underdetermined systems - Create (and do not display) a 23 random matrices A1 with each entry between 5 and 5 using the command randi - Create (and do not display) a 21 vector b with each entry between 5 and 5 using the same command randi - Display the augmented matrix [A1 b] - Call LS_solution for the system A1x = b - Repeat the process above for the systems A2x=b and A3x=b (b) Explain why you would expect most underdetermined linear systems to have infinitely many solutions. Does an underdetermined linear system always have infinitely many solutions? If not, give an example. (c) For overdetermined systems * repeat the same process - Create (and do not display) a 32 random matrices A1 with each entry between 5 and 5 using the command randi - create (and do not display) a 31 vector b with each entry between 5 and 5 using the same command randi - Display the augmented matrix [A1 b] - Call LS_solution for each system A1x = b - Repeat the process above for the systems A2x=b and A3x=b (d) Explain why you would expect most overdetermined linear systems to be inconsistent. Can an overdetermined linear system have one solution or infinitely many solutions? Give examples. \% create three 23 matrices (A1, A2,A3 ) of random numbers between 5 and 5 A1= A2= A3= % create a 21 vector b of random numbers between 5 and 5 b % Call LS_solution for the system A1x=b to determine the number of o solutions of the system [m, ] = size(A1); [A1 b] LS_solution() \& repeat the process for the systems A2x=b and A3x=b 3 (b) We expect most underdeterminded systems to have infinitely many solutions because ... Does an underdetermined linear system always have infinitely many solutions? If not, give an example. \#3 (c) \& repeat the process in part (a) with 32 matrices A1,A2,A3, and a 31 vecto \#3 (d) We expect most overdeterminded systems to be inconsistent because ... Can an overdetermined linear system have one solution or infinitely many solutions? - one solution - give an example here ... (Do you know how to type math equations in MATLAB?) or - infinitely many solutions - give an example here