CoCalc -- 0008.ptx

banks / tbil-la / __build__ / E2 / 0008.ptx
²³¹²⁸ views
ubuntu2004
1
<exercise checkit-seed="0008" checkit-slug="E2" checkit-title="Reduced row echelon form">
2
  <statement>
3
    <ol>
4
      <li>Show that <me>\operatorname{RREF} \left[\begin{array}{ccc}
5
0 &amp; 5 &amp; 5 \\
6
-1 &amp; -3 &amp; -4 \\
7
-1 &amp; 1 &amp; 0 \\
8
-1 &amp; -8 &amp; -9 \\
9
-1 &amp; -2 &amp; -3
10
\end{array}\right] = \left[\begin{array}{ccc}
11
1 &amp; 0 &amp; 1 \\
12
0 &amp; 1 &amp; 1 \\
13
0 &amp; 0 &amp; 0 \\
14
0 &amp; 0 &amp; 0 \\
15
0 &amp; 0 &amp; 0
16
\end{array}\right] .</me></li>
17
      <li>Explain why the matrix <m>B= \left[\begin{array}{ccc}
18
-3 &amp; 15 &amp; 0 \\
19
0 &amp; 0 &amp; 1 \\
20
0 &amp; 0 &amp; 0 \\
21
0 &amp; 0 &amp; 0 \\
22
0 &amp; 0 &amp; 0
23
\end{array}\right] </m> is or is not in reduced row echelon form.</li>
24
    </ol>
25
  </statement>
26
  <answer>
27
    <ol>
28
      <li>
29
        <m>\operatorname{RREF} \left[\begin{array}{ccc}
30
0 &amp; 5 &amp; 5 \\
31
-1 &amp; -3 &amp; -4 \\
32
-1 &amp; 1 &amp; 0 \\
33
-1 &amp; -8 &amp; -9 \\
34
-1 &amp; -2 &amp; -3
35
\end{array}\right] = \left[\begin{array}{ccc}
36
1 &amp; 0 &amp; 1 \\
37
0 &amp; 1 &amp; 1 \\
38
0 &amp; 0 &amp; 0 \\
39
0 &amp; 0 &amp; 0 \\
40
0 &amp; 0 &amp; 0
41
\end{array}\right] .</m>
42
      </li>
43
      <li><m>B</m> is
44
                
45
                        not in reduced row echelon form because
46
                        
47
                                the pivots are not all <m>1</m>.
48
                            </li>
49
    </ol>
50
  </answer>
51
</exercise>
52

53

54
Product

Resources

Company
