Exercises

1.: Calculate ranks of the following matrices.

$\begin{displaymath} \left( \begin{array}{cccc} 2 & 1 & 1 & 0\ 1 & 2 & -1 & 0... ...0 & 0 & 1 & 2 & 4\ 3 & 3 & 3 & 2 & 10\ \end{array}\right) \end{displaymath}$
2.: Find a basis for

$\begin{displaymath} \left( \begin{array}{cccc} 1 & 1 & 1 & 1 \ 1 & 2 & 2 &... ...3 \ 3 & 2 & 2 & 3 \ 8 & 6 & 6 & 8 \ \end{array}\right) \end{displaymath}$
3.: Find a basis for

$\begin{displaymath} \left( \begin{array}{ccccc} 1 & 0 & -5 & 1 & 4 \ -2 & 1 & 6 & -2 & -2 \ 0 & 2 & -8 & 1 & 9 \end{array}\right) \end{displaymath}$

Sergey Nikitin 2005-01-31