1. Give an example of a linear system of equations corresponding to each of the following: (a) A system of linear equations in 7 variables that has no solution. (b) A system of linear equations in 8 variables that has a unique solution. (c) A system of linear equations in 9 variables with infinity many solu- tions in 4 free variables. 2. A prize fund has been announced for a person to solve a linear system of equations using a computer, you have a very good computer and need to decide should you use it to mine the new popular Patrick coin or solve the linear systems. You quickly discover that you need to determine how many operations a computer needs to preform to solve a given system of equations. (a) Given a system of three linear equations, what is the most number of operations a computer would need to solve the system. (b) The competition outlined above will be asking you to solve systems of n equations in m unknowns, assuming your computer can preform one operation per second, how long would it take to solve this system