решить систему линейных уравнений по правилу крамера:
x+y-z=0
2x+3y-2z=2
3x-2y =1
Найдём значения Δ, Δ1, Δ2 и Δ3
Δ = определитель матрицы = 3
Δ1 = определитель матрицы = 5
Δ2 = определитель матрицы = 6
Δ3 = определитель матрицы = 11
Получим:
X = Δ1/Δ = 5/3
Y = Δ2/Δ = 6/3 = 2
Z = Δ3/Δ = 11/3
![\left[\begin{array}{ccc}1&1&-1\\2&3&-2\\3&-2&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%26-1%5C%5C2%263%26-2%5C%5C3%26-2%260%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{ccc}1&1&-1\\2&3&-2\\3&-2&0\end{array}\right]")
= 3![\left[\begin{array}{ccc}0&1&-1\\2&3&-2\\1&-2&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%261%26-1%5C%5C2%263%26-2%5C%5C1%26-2%260%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{ccc}0&1&-1\\2&3&-2\\1&-2&0\end{array}\right]")
= 5![\left[\begin{array}{ccc}1&0&-1\\2&2&-2\\3&1&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26-1%5C%5C2%262%26-2%5C%5C3%261%260%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{ccc}1&0&-1\\2&2&-2\\3&1&0\end{array}\right]")
= 6 ![\left[\begin{array}{ccc}1&1&0\\2&3&2\\3&-2&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%261%260%5C%5C2%263%262%5C%5C3%26-2%261%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{ccc}1&1&0\\2&3&2\\3&-2&1\end{array}\right]")
= 11