Assess students' ability to apply the Gram–Schmidt process to finite sets in inner product spaces: perform step-by-step orthonormalization of given vectors (including detection and handling of linear dependence), compute orthogonal projections, verify orthonormality and span preservation, and adapt the procedure to a nonstandard inner product. Include one explicit computation (three vectors in R^3) and one short proof-level task (showing the process preserves span).