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Next: Problems on Inhomogeneous Systems Up: Solutions to Supplementary Homework Previous: Problems on Bases

Problems on Row Reduction

1.

\begin{displaymath}\left[\begin{array}{rr}1&2\\ 3&4\end{array}\right]
\rightarr...
...ightarrow
\left[\begin{array}{rr}1&0\\ 0&1\end{array}\right].
\end{displaymath}

2.

\begin{displaymath}\left[\begin{array}{rr}1&2\\ 3&4\\ 5&6\end{array}\right]
\ri...
...row
\left[\begin{array}{rr}1&0\\ 0&1\\ 0&0\end{array}\right].
\end{displaymath}

3.

\begin{displaymath}\left[\begin{array}{rrrr}1&2&-1&2\\ 1&1&1&1\end{array}\right]...
...\left[\begin{array}{rrrr}1&0&3&0\\ 0&1&-2&1\end{array}\right].
\end{displaymath}

4.

\begin{eqnarray*}&&\left[\begin{array}{rrr}0&3&1\\ 1&1&1\\ 1&0&0\end{array}\righ...
... \left[\begin{array}{rrr}1&0&0\\ 0&1&0\\ 0&0&1\end{array}\right]
\end{eqnarray*}


5.
octave:1> A=[1,2,3,2,1;0,5,-1,3,4;1,2,-1,5,3;2,9,1,10,8;3,11,0,15,11]
A =

    1    2    3    2    1
    0    5   -1    3    4
    1    2   -1    5    3
    2    9    1   10    8
    3   11    0   15   11

octave:2> rref(A)
ans =

   1.00000   0.00000   0.00000   3.35000   1.10000
   0.00000   1.00000   0.00000   0.45000   0.70000
   0.00000   0.00000   1.00000  -0.75000  -0.50000
   0.00000   0.00000   0.00000   0.00000   0.00000
   0.00000   0.00000   0.00000   0.00000   0.00000

6.
octave:3> B=[2.1,3.14,1.1,-0.4,0.1;-2.3,3.1,3.6,12.1,-1;
> 0,1.2,0,-0.22,0.1;0.23,0.21,-0.1,-3.4,2.0;0.34,0.1,-4.1,-2.2,1.0]
B =

    2.10000    3.14000    1.10000   -0.40000    0.10000
   -2.30000    3.10000    3.60000   12.10000   -1.00000
    0.00000    1.20000    0.00000   -0.22000    0.10000
    0.23000    0.21000   -0.10000   -3.40000    2.00000
    0.34000    0.10000   -4.10000   -2.20000    1.00000

octave:4> rref(B)
ans =

  1  0  0  0  0
  0  1  0  0  0
  0  0  1  0  0
  0  0  0  1  0
  0  0  0  0  1



Frank Beatrous
1998-09-21