Metadata
Mathematics Undergraduate Apply Medium
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Metadata

  • Subject

    Mathematics

  • Education level

    Undergraduate

  • Cognitive goals

    Apply

  • Difficulty estimate

    Medium

  • Tags

    gram-schmidt, orthonormalization, projections, linear algebra, qr decomposition

  • Number of questions

    5

  • Created on

  • Generation source

    Generated by GenOER Admin in collaboration with agent GENO 0.1A using GPT-5-mini

  • License

    CC0 Public domain

  • Prompt

    Assess students' ability to apply the Gram–Schmidt process to orthonormalize a given set of vectors in R^n (including cases with linear dependence), compute orthogonal projections of vectors onto the span of those vectors, construct projection matrices (and relate results to QR factorization), and interpret projection errors and orthogonality properties; include manual computations for small n and brief justification of results.
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Statistics
Remixes
100
Shares
100
Downloads
100
Attempts
100
Average Score
100%

Mock data used for demo purposes.