The Induced Dimension Reduction(s) method (or the IDR(s) method) is an example of an iterative method used for solving systems of linear equations. Projection methods are a special type of iterative method. They find an approximate solution in a subspace (the right subspace) by requiring that the residual is orthogonal to another subspace (the left subspace). In this thesis we investigate how we can implement IDR(s) as a projection method. We call this method IDR(s), which stands for Projected IDR(s).We present an implementation of PIDR(s) for solving systems of linear equations and for solving eigenvalue problems. These implementations are not meant to be optimal, but they are used to show that IDR(s) can indeed be seen as a projection method.