В матрице Х должно быть столько же строк, сколько столбцов в первой матрице, т.е. 2.
Кроме этого, в матрице, являющейся произведением двух матриц, столько же столбцов, сколько столбцов во второй матрице. Значит в матрице Х 3 столбца.
![X=\left[\begin{array}{ccc}x_{11}&x_{12}&x_{13}\\x_{21}&x_{22}&x_{23}\end{array}\right]](https://tex.z-dn.net/?f=X%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx_%7B11%7D%26x_%7B12%7D%26x_%7B13%7D%5C%5Cx_%7B21%7D%26x_%7B22%7D%26x_%7B23%7D%5Cend%7Barray%7D%5Cright%5D "X=\left[\begin{array}{ccc}x_{11}&x_{12}&x_{13}\\x_{21}&x_{22}&x_{23}\end{array}\right]")
![\left[\begin{array}{ccc}1&-2\\-3&4\end{array}\right]*\left[\begin{array}{ccc}x_{11}&x_{12}&x_{13}\\x_{21}&x_{22}&x_{23}\end{array}\right]=\\ \\=\left[\begin{array}{ccc}x_{11}-2x_{21}&x_{12}-2x_{22}&x_{13}-2x_{23}\\-3x_{11}+4x_{21}&-3x_{12}+4x_{22}&-3x_{13}+4x_{23}\end{array}\right]=\left[\begin{array}{ccc}-2&3&5\\3&-1&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-2%5C%5C-3%264%5Cend%7Barray%7D%5Cright%5D%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx_%7B11%7D%26x_%7B12%7D%26x_%7B13%7D%5C%5Cx_%7B21%7D%26x_%7B22%7D%26x_%7B23%7D%5Cend%7Barray%7D%5Cright%5D%3D%5C%5C%20%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx_%7B11%7D-2x_%7B21%7D%26x_%7B12%7D-2x_%7B22%7D%26x_%7B13%7D-2x_%7B23%7D%5C%5C-3x_%7B11%7D%2B4x_%7B21%7D%26-3x_%7B12%7D%2B4x_%7B22%7D%26-3x_%7B13%7D%2B4x_%7B23%7D%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%263%265%5C%5C3%26-1%260%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{ccc}1&-2\\-3&4\end{array}\right]*\left[\begin{array}{ccc}x_{11}&x_{12}&x_{13}\\x_{21}&x_{22}&x_{23}\end{array}\right]=\\ \\=\left[\begin{array}{ccc}x_{11}-2x_{21}&x_{12}-2x_{22}&x_{13}-2x_{23}\\-3x_{11}+4x_{21}&-3x_{12}+4x_{22}&-3x_{13}+4x_{23}\end{array}\right]=\left[\begin{array}{ccc}-2&3&5\\3&-1&0\end{array}\right]")
Приравниваем соответствующие элементы двух последних матриц.
![\left[\begin{array}{ccc}x_{11}-2x_{21}=-2&x_{12}-2x_{22}=3&x_{13}-2x_{23}=5\\-3x_{11}+4x_{21}=3&-3x_{12}+4x_{22}=-1&-3x_{13}+4x_{23}=0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx_%7B11%7D-2x_%7B21%7D%3D-2%26x_%7B12%7D-2x_%7B22%7D%3D3%26x_%7B13%7D-2x_%7B23%7D%3D5%5C%5C-3x_%7B11%7D%2B4x_%7B21%7D%3D3%26-3x_%7B12%7D%2B4x_%7B22%7D%3D-1%26-3x_%7B13%7D%2B4x_%7B23%7D%3D0%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{ccc}x_{11}-2x_{21}=-2&x_{12}-2x_{22}=3&x_{13}-2x_{23}=5\\-3x_{11}+4x_{21}=3&-3x_{12}+4x_{22}=-1&-3x_{13}+4x_{23}=0\end{array}\right]")
Составляем системы уравнений по столбцам. Получатся системы из двух уравнений с двумя неизвестными.
![X=\left[\begin{array}{ccc}1&-5&-10\\1,5&-4&-7,5\end{array}\right]](https://tex.z-dn.net/?f=X%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-5%26-10%5C%5C1%2C5%26-4%26-7%2C5%5Cend%7Barray%7D%5Cright%5D "X=\left[\begin{array}{ccc}1&-5&-10\\1,5&-4&-7,5\end{array}\right]")
Проверка:
![\left[\begin{array}{ccc}1&-2\\-3&4\end{array}\right] *\left[\begin{array}{ccc}1&-5&-10\\1,5&-4&-7,5\end{array}\right] =\\\\=\left[\begin{array}{ccc}1*1+(-2)*1,5&1*(-5)+(-2)*(-4)&1*(-10)+(-2)*(-7,5)\\-3*1+4*1,5&-3*(-5)+4*(-4)&-3*(-10)+4*(-7,5)\end{array}\right] \\\\ =\left[\begin{array}{ccc}-2&3&5\\3&-1&0\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-2%5C%5C-3%264%5Cend%7Barray%7D%5Cright%5D%20%2A%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-5%26-10%5C%5C1%2C5%26-4%26-7%2C5%5Cend%7Barray%7D%5Cright%5D%20%3D%5C%5C%5C%5C%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%2A1%2B%28-2%29%2A1%2C5%261%2A%28-5%29%2B%28-2%29%2A%28-4%29%261%2A%28-10%29%2B%28-2%29%2A%28-7%2C5%29%5C%5C-3%2A1%2B4%2A1%2C5%26-3%2A%28-5%29%2B4%2A%28-4%29%26-3%2A%28-10%29%2B4%2A%28-7%2C5%29%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%263%265%5C%5C3%26-1%260%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{ccc}1&-2\\-3&4\end{array}\right] *\left[\begin{array}{ccc}1&-5&-10\\1,5&-4&-7,5\end{array}\right] =\\\\=\left[\begin{array}{ccc}1*1+(-2)*1,5&1*(-5)+(-2)*(-4)&1*(-10)+(-2)*(-7,5)\\-3*1+4*1,5&-3*(-5)+4*(-4)&-3*(-10)+4*(-7,5)\end{array}\right] \\\\ =\left[\begin{array}{ccc}-2&3&5\\3&-1&0\end{array}\right]")
Ответ: