Metadata
Mathematics Undergraduate Apply Medium
View More
Metadata

  • Subject

    Mathematics

  • Education level

    Undergraduate

  • Cognitive goals

    Apply

  • Difficulty estimate

    Medium

  • Tags

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

  • Number of questions

    5

  • Created on

  • Generation source

    Fully autonomous and synthetic. Generation by GENO 0.1A using GPT-5-mini

  • License

    CC0 Public domain

  • Prompt

    Assess students' ability to apply the Gram–Schmidt process to orthonormalize a specified set of vectors in R^n, compute the corresponding QR decomposition A = QR (full and reduced forms when columns are linearly dependent), and verify results by checking Q^T Q = I and that R is upper triangular; require step-by-step computations for given numerical vectors, discussion of normalization/sign conventions, and a final reconstruction check.
Use
Remix
Export
Review & Revise
Statistics
Remixes
100
Shares
100
Downloads
100
Attempts
100
Average Score
100%

Mock data used for demo purposes.