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{
    "url": "https://numbas.mathcentre.ac.uk/api/questions/12035/?format=api",
    "name": "Do three given vectors form a spanning set and are they linearly independent?",
    "published": true,
    "project": "https://numbas.mathcentre.ac.uk/api/projects/601/?format=api",
    "author": {
        "url": "https://numbas.mathcentre.ac.uk/api/users/697/?format=api",
        "profile": "https://numbas.mathcentre.ac.uk/accounts/profile/697/?format=api",
        "full_name": "Newcastle University Mathematics and Statistics",
        "pk": 697,
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    "edit": "https://numbas.mathcentre.ac.uk/question/12035/do-three-given-vectors-form-a-spanning-set-and-are/?format=api",
    "preview": "https://numbas.mathcentre.ac.uk/question/12035/do-three-given-vectors-form-a-spanning-set-and-are/preview/?format=api",
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    "source": "https://numbas.mathcentre.ac.uk/question/12035/do-three-given-vectors-form-a-spanning-set-and-are.exam?format=api",
    "metadata": {
        "notes": "<p><strong>11/02/2013:</strong></p>\n                <p>Finished first draft. Need to resolve the display of row vectors etc.</p>\n                <p>Display of linear equations difficult to format e.g. variables under one another as got to use \\simplify where there are randomised coefficients.&nbsp;</p>",
        "licence": "Creative Commons Attribution 4.0 International",
        "description": "<p>Given the following three vectors $\\textbf{v}_1,\\;\\textbf{v}_2,\\;\\textbf{v}_3$ Find out whether they are a linearly independent set are not. Also if linearly dependent find the relationship $\\textbf{v}_{r}=p\\textbf{v}_{s}+q\\textbf{v}_{t}$ for suitable $r,\\;s,\\;t$ and integers $p,\\;q$.</p>"
    },
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}