PreTeXt Sample Book: Abstract Algebra (SAMPLE ONLY)

<exercises xml:id="matching-exercises">
  <title>Matching Exercises</title>

  <exercise xml:id="matching-one" label="matching-dates">
    <title>Matching Problem, Dates</title>
    <idx>matching US dates</idx>
    <statement>
      <p>
        Match each event in United States history with the year it happened.
      </p>
    </statement>
    <feedback>
      <p>
        Review
        <url href="https://www.britannica.com/list/25-decade-defining-events-in-us-history" visual="www.britannica.com/list/25-decade-defining-events-in-us-history">Encyclopedia Brittania, 25 Decade-Defining Events in U.S. History</url>
        url.
      </p>
    </feedback>
    <matches>
    <match order="4">
    <premise>Monroe Doctrine</premise>
    <response>1823</response>
    </match>
    <match order="3">
    <premise>Haymarket Riot</premise>
    <response>1886</response>
    </match>
    <match order="1">
    <premise>Louisiana Purchase</premise>
    <response>1803</response>
    </match>
    <match order="2">
    <premise>Battle of Gettysburg</premise>
    <response>1863</response>
    </match>
    </matches>
  </exercise>
  <exercise label="matching-derivatives">
    <title>Matching Problem, Derivatives</title>
    <idx>matching derivatives</idx>
    <statement>
      <p>
        Match each function with its derivative.
      </p>
    </statement>
    <feedback>
      <p>
        Did you compute the derivative of each function in the premises (left column)?
      </p>
    </feedback>
    <matches>
    <match order="1">
    <premise><m>x^3-6x^2+5</m></premise>
    <response><m>3x^2-12x</m></response>
    </match>
    <match order="3">
    <premise><m>x^{-3}</m></premise>
    <response><m>-3x^{-4}</m></response>
    </match>
    <match order="2">
    <premise><m>(x+1)^2</m></premise>
    <response><m>2x+2</m></response>
    </match>
    </matches>
  </exercise>
  <exercise label="matching-bases">
    <title>Matching Problem, Linear Algebra</title>
    <idx>matching bases and subspaces</idx>
    <statement>
      <p>
        Match each subspace with a basis for that subspace.
        (You may assume that each set is really a basis for at least one of the subspaces.)
      </p>
    </statement>
    <feedback>
      <p>
        Each putative basis is a subset of exactly one of the three subspaces.
        So for each subspace,
        two of the three sets can be ruled out by simply testing that the vectors of the basis are members of the subspace,
        via the membership criteria.
      </p>
    </feedback>
    <matches>
    <match order="2">
    <premise><m>\left\{\langle x,y,z\rangle\mid - y + z = 0\right\}</m></premise>
    <response><m>\left\{\langle -4, 3, 3\rangle, \langle 3, -2, -2 \rangle\right\}</m></response>
    </match>
    <match order="2">
    <premise><m>\left\{\langle x,y,z\rangle\mid -3x - 5y + z = 0\right\}</m></premise>
    <response><m>\left\{\langle -4, 3, 3\rangle, \langle 5, -4, -5 \rangle\right\}</m></response>
    </match>
    <match order="2">
    <premise><m>\left\{\langle x,y,z\rangle\mid -2x - 5y + 2z = 0\right\}</m></premise>
    <response><m>\left\{\langle 3, -2, -2 \rangle, \langle 5, -4, -5 \rangle\right\}</m></response>
    </match>
    </matches>
    <hint>
      <p>
        For openers, a basis for a subspace must be a
        <em>subset</em> of the subspace.
      </p>
    </hint>
  </exercise>
  <exercise label="matching-function-types">
    <title>Matching Problem, Function Types</title>
    <idx>matching function types</idx>
    <statement>
      <p>
        Sort the following functions into their correct categories. [Ed.
        As of 2024-10-07 the following problem is not expected to render and function properly.
        It is here to aid development work.
        Nothing to see here.]
      </p>
    </statement>
    <feedback>
      <p>
        Review
        <url href="https://activecalculus.org/prelude/sec-changing-linear.html" visual="A precalculus textbook that could help">Active Prelude to Calculus</url>
        url.
      </p>
    </feedback>
    <matches>
    <match>
    <response>Linear</response>
    <premise order="4"><m>y=5x+3</m></premise>
    <premise order="5"><m>\pi x - 6y = \sqrt{2}</m></premise>
    <premise order="6"><m>y=\frac{-1}{2}x+e</m></premise>
    </match>
    <match>
    <response>Quadratic</response>
    </match>
    <match>
    <premise order="7"><m>y=x^3-x</m></premise>
    </match>
    <match>
    <response>Exponential</response>
    <premise order="1"><m>y=2^x</m></premise>
    </match>
    <match>
    <response>Power</response>
    <premise order="2"><m>y=x^3</m></premise>
    <premise order="3"><m>y=\sqrt{x}</m></premise>
    </match>
    </matches>
  </exercise>
</exercises>