Due to the rapid growth of the Internet, there has been a rising interest in using the Web as an interface to develop various applications over computational Grid environments. The purpose of this work is to develop a Grid-aware Web interface for linear algebra tasks with advanced service trading. Developing efficient and portable codes, requires users to face parallel computing and programming and to make use of different standard libraries, such as the BLAS [1], LAPACK [2] and ScaLAPACK [3] in order to solve computational tasks related to linear algebra. For this purpose, a scientific computing environment based on a Web interface is described that allows users to perform their linear algebra tasks without explicitly calling the above mentioned libraries and softwarep tools, as well as without installing any piece of software on local computers: users enter algebraic formula (such as in Matlab or Scilab [4]) that are evaluated for determining the combinations of services answering the user request. Services are then executed locally or over the Grid using the Distributed Interactive Engineering Toolbox (DIET) [5] middleware.