Oblicz wyznacznik macierzy
Otrzymałeś(aś) rozwiązanie do zamieszczonego zadania? - podziękuj autorowi rozwiązania! Kliknij
\(\begin{vmatrix} 2& 1&2& 3& 2&\\3& -2& 7& 5& -1&\\3& -1& -5& -3& -2&\\5& -6& 4& 2& -4&\\2& -3& 3& 1& -2&\end{vmatrix}\)
\(w_{1}+2w_{2}, w_{3}-2w_{2}, w_{4}-4w_{2}, w_{5}-2w_{2} = \begin{vmatrix} 8& -3& 16& 13& 0&\\3& -2& 7& 5& -1&\\-3& 3& -19& -13& 0&\\-7& 2& -24& -18& 0&\\-4& 1& -11& -9& 0&\end{vmatrix}\)
\(= (-1)^{5+2} \cdot (-1) \cdot \det \begin{vmatrix} 8& -3& 16& 13& \\-3& 3& -19& -13& \\-7& 2& -24& -18& \\-4& 1& -11& -9& \end{vmatrix}\)
\(k_{1} + 4k_{2}, k_{3}+11k_{2}. k_{4}+9k_{2} = \begin{vmatrix} -4& -3& -17& -14& \\9& 3& 14& 14& \\1& 2& -2& 0& \\0& 1& 0& 0& \end{vmatrix} = (-1)^{4+2} \cdot \det \begin{vmatrix} -4& -17& -14& \\9& 14& 14& \\1& -2& 0& \end{vmatrix} = \\=0-238+252+196-112-0 = 98\)
\(w_{1}+2w_{2}, w_{3}-2w_{2}, w_{4}-4w_{2}, w_{5}-2w_{2} = \begin{vmatrix} 8& -3& 16& 13& 0&\\3& -2& 7& 5& -1&\\-3& 3& -19& -13& 0&\\-7& 2& -24& -18& 0&\\-4& 1& -11& -9& 0&\end{vmatrix}\)
\(= (-1)^{5+2} \cdot (-1) \cdot \det \begin{vmatrix} 8& -3& 16& 13& \\-3& 3& -19& -13& \\-7& 2& -24& -18& \\-4& 1& -11& -9& \end{vmatrix}\)
\(k_{1} + 4k_{2}, k_{3}+11k_{2}. k_{4}+9k_{2} = \begin{vmatrix} -4& -3& -17& -14& \\9& 3& 14& 14& \\1& 2& -2& 0& \\0& 1& 0& 0& \end{vmatrix} = (-1)^{4+2} \cdot \det \begin{vmatrix} -4& -17& -14& \\9& 14& 14& \\1& -2& 0& \end{vmatrix} = \\=0-238+252+196-112-0 = 98\)