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<exercise checkit-seed="0008" checkit-slug="E1" checkit-title="Linear systems, vector equations, and augmented matrices">

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  <statement>

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        <p>Consider the vector equation.</p>

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

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-4 \\

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5 \\

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-4 \\

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2

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

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-4 \\

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5 \\

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-4 \\

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2

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

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-1 \\

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1 \\

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2 \\

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4

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

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-5 \\

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7 \\

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-14 \\

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-8

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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 vector equation. </li>

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            <li> Write an augmented matrix corresponding to this vector equation. </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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 -4 \, x_{1} &amp;  -  &amp; 4 \, x_{2} &amp;  -  &amp; x_{3} &amp; = &amp; -5 \\

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 5 \, x_{1} &amp;  +  &amp; 5 \, x_{2} &amp;  +  &amp; x_{3} &amp; = &amp; 7 \\

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 -4 \, x_{1} &amp;  -  &amp; 4 \, x_{2} &amp;  +  &amp; 2 \, x_{3} &amp; = &amp; -14 \\

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 2 \, x_{1} &amp;  +  &amp; 2 \, x_{2} &amp;  +  &amp; 4 \, x_{3} &amp; = &amp; -8 \\

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

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

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-4 &amp; -4 &amp; -1 &amp; -5 \\

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5 &amp; 5 &amp; 1 &amp; 7 \\

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-4 &amp; -4 &amp; 2 &amp; -14 \\

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2 &amp; 2 &amp; 4 &amp; -8

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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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