Cvičenia


13. Gaussovou eliminačnou metódou určte riešenia nasledovných sústav lineárnych rovníc.
a)

\begin{displaymath}
\begin{array}{rrrrrrr}
& & x_2 & + & x_3 & = & 2 \\
-x_1 ...
...3 & = & 1 \\
x_1 & + & 2x_2 & + & x_3 & = & 1 \\
\end{array}\end{displaymath}

b)

\begin{displaymath}
\begin{array}{rrrrrrr}
6x_1 & - & x_2 & - & x_3 & = & 11 \\...
...= & 32 \\
-x_1 & - & 2x_2 & + & 6x_3 & = & 42 \\
\end{array}\end{displaymath}

c)

\begin{displaymath}
\begin{array}{rrrrrrr}
2x_1 & + & 3x_2 & + & 5x_3 & = & 10 ...
... & = & 3 \\
x_1 & + & 2x_2 & + & 2x_3 & = & 3 \\
\end{array}\end{displaymath}

d)

\begin{displaymath}
\begin{array}{rrrrrrr}
4x_1 & - & 3x_2 & + & 2x_3 & = & -4 ...
...= & -1 \\
5x_1 & - & 3x_2 & + & 2x_3 & = & -3 \\
\end{array}\end{displaymath}

e)

\begin{displaymath}
\begin{array}{rrrrrrr}
5x_1 & - & 6x_2 & + & 4x_3 & = & 3 \...
...& = & 2 \\
4x_1 & - & 5x_2 & + & 2x_3 & = & 1 \\
\end{array}\end{displaymath}

f)

\begin{displaymath}
\begin{array}{rrrrrrr}
5x_1 & + & 2x_2 & + & 3x_3 & = & -2 ...
...= & 0 \\
3x_1 & + & 4x_2 & + & 2x_3 & = & -10 \\
\end{array}\end{displaymath}

g)

\begin{displaymath}
\begin{array}{rrrrrrrrr}
2x_1 & + & 2x_2 & - & x_3 & + & x_...
...
3x_1 & + & 3x_2 & - & 2x_3 & + & 2x_4 & = & 6 \\
\end{array}\end{displaymath}

h)

\begin{displaymath}
\begin{array}{rrrrrrrrr}
2x_1 & + & 3x_2 & + & 11x_3 & + & ...
...
x_1 & + & x_2 & - & 3x_3 & + & 4x_4 & = & -3 \\
\end{array}\end{displaymath}

i)

\begin{displaymath}
\begin{array}{rrrrrrrrr}
2x_1 & + & 5x_2 & + & 4x_3 & + & x...
... 3x_1 & + & 8x_2 & + & 9x_3 & + & 2x_4 & = & 37 \\
\end{array}\end{displaymath}