The way in which computer algebra systems, such as Maple, have made the study of complex problems accessible to undergraduate mathematicians with modest computational skills is illustrated by some large matrix calculations, which arise from representing the Earth's surface by digital elevation models. Such problems are often considered to lie in the field of computer mapping and thus addressed by geographical information systems. The problems include simple identification of local maximum points, visualization by cross-sectional profiles, contour maps and three-dimensional views, consideration of the visual impact of the placement of large buildings and issues arising from reservoir creation. Motion through a virtual landscape can be simulated by an animation facility. This approach has been successful with first year students: the 'real world' problems considered are more accessible than many alternatives, and the attraction of using large matrices is retained.