1. Consider x = (1,0,0,1) and y = (0,1,1,0) as real-valued, 4-dimensional vectors. Given an arbitrary real-valued vector z = (z, Z, Z3, Z4), how can you tell if z can be written as a linear combination of x and y or not? Describe an algorithm that takes in an input vector z and output "yes" if it can be written as a linear combination of x and y, and outputs "no" otherwise.