For all problems, include one or two examples to demonstrate that your function works as intended. For all functions, include code that checks whether the arguments satisfy the specifications in the problem. If not, the code should throw an error with a meaningful error code. Code up the algorithm yourself whenever possible. For example, you should implement the forward solving algorithm instead of calling forwardsolve 1. Write a function that takes in a 'n' by `n` lower triangular matrix `L`, and an `n by 1 vector `b`, and returns the solution to 'L x = b`. 2. Write a function that takes in a `n by `n` upper triangular matrix U`, and an `n` by 1 vector b`, and returns the solution to 'U x = b`. 3. Write a function that takes in an `n by `n matrix A and returns the lower triangular matrix `L` such that `A = L LAT`. If the calculation fails because you cannot take the square root of a negative number, your function should return the current upper-left corner of Land print a warning message.