stosujac eliminacje gaussa rozwiazac uklad

[olak87]

Stosujac eleiminacje gaussa rozwiazac uklad


\(\displaystyle{ \left\{\begin{array}{l}x + 3y - 7z = -9 \\-2x - 4y +8z = 12\\-x - 3y + 5z = 7 \end{array}}\)

[soku11]

Mamy wiec macierz, na ktorej robimy przeksztalcenia:
\(\displaystyle{ \left[\begin{array}{ccc|c}
1&3&-7&-9\\
-2&-4&8&12\\
-1&-3&5&7\end{array}\right]\\
ft[\begin{array}{ccc|c}
1&3&-7&-9\\
1&2&-4&-6\\
-1&-3&5&7\end{array}\right]\\
ft[\begin{array}{ccc|c}
0&0&-2&-2\\
1&2&-4&-6\\
-1&-3&5&7\end{array}\right]\\
ft[\begin{array}{ccc|c}
0&0&-2&-2\\
0&-1&1&1\\
-1&-3&5&7\end{array}\right]\\
ft[\begin{array}{ccc|c}
1&3&-5&-7\\
0&1&-1&-1\\
0&0&1&1\\
\end{array}\right]\\}\)

Stad:
\(\displaystyle{ \begin{cases}
z=1\\
y-z=-1\\
x+3y-5z=-7\end{cases}\\
\begin{cases}
z=1\\
y=0\\
x=-2\end{cases}\\}\)

POZDRO