1. Part 1 - Solutions of systems of linear equations By considering random matrices of appropriate sizes, find emperical evidence that substantiate the following statements. (In this part, m and n are both integers and both are greater than 6, so 7 or larger). (a) A system of n linear equations in n unknowns typically has a unique solution. (b) A system of m linear equations in n unknowns, where m > n, typically has no solution. (c) A system of m linear equations in n unknowns, where m < n, typically has many solutions. Give examples of exceptions for each case (but for this part, you can use integers m and n that need only be larger than 2, so 3 or larger).