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<exercise checkit-seed="0004" checkit-slug="E1" checkit-title="Linear systems, vector equations, and augmented matrices">

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  <statement>

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        <p> Consider the augmented matrix </p>

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              <me>\left[\begin{array}{ccc|c}

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1 &amp; 0 &amp; 2 &amp; 3 \\

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-2 &amp; 1 &amp; -5 &amp; -2 \\

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-3 &amp; 1 &amp; -7 &amp; -4 \\

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-2 &amp; 1 &amp; -5 &amp; -5

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\end{array}\right]</me>

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         <ol>

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            <li> Write a system of scalar equations corresponding to this augmented matrix. </li>

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            <li> Write a vector equation corresponding to this augmented matrix. </li>

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        </ol>

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  </statement>

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  <answer>

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     <ol>

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                <li><me>\begin{matrix}

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 x &amp;  &amp;  &amp;  +  &amp; 2 \, z &amp; = &amp; 3 \\

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 -2 \, x &amp;  +  &amp; y &amp;  -  &amp; 5 \, z &amp; = &amp; -2 \\

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 -3 \, x &amp;  +  &amp; y &amp;  -  &amp; 7 \, z &amp; = &amp; -4 \\

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 -2 \, x &amp;  +  &amp; y &amp;  -  &amp; 5 \, z &amp; = &amp; -5 \\

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 \end{matrix}</me></li>

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                <li><me>x_{1} \left[\begin{array}{c}

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1 \\

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-2 \\

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-3 \\

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-2

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\end{array}\right] + x_{2} \left[\begin{array}{c}

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0 \\

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1 \\

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1 \\

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1

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\end{array}\right] + x_{3} \left[\begin{array}{c}

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2 \\

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-5 \\

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-7 \\

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-5

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\end{array}\right] = \left[\begin{array}{c}

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3 \\

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-2 \\

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-4 \\

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-5

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\end{array}\right]</me></li>

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      </ol>

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    </answer>

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</exercise>

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