# Finding a Transformation Matrix to yield the basis

 P: 351 I don't really think you're looking for a transformation matrix here. You have some vector space, with a vector u. There are a bunch of vectors (an infinite number, in fact!) in the space that solve the equation $u'' = u$. What you want is a way to write down any vector that solves that equation as the sum of two other vectors (that you are going to find). Now, what vectors solve this equation?