Срочно, пожалуйста помогите с подробным решением!найти f(A), если:f(x)=3x^3-2x+4 A= 1 -2; 0 3
Матрица А записана справа по строчкам. Это задача на нахождение значения матричного многочлена.
Аналогично значению функции в точке, только действия другие.
Находим
Тогда
https://znanija.com/task/31679411
реши пж
Точки здесь нет. Это задача на нахождение значения матричного многочлена, матрица второго порядка, написана справа по строкам.
Вместо -3 должно быть 5
![A^{2}=\left[\begin{array}{cc}1&-2\\0&3\end{array}\right] \cdot\left[\begin{array}{cc}1&-2\\0&3\end{array}\right] =\left[\begin{array}{cc}1\cdot1-2\cdot0&1\cdot(-2)-2\cdot3\\0\cdot1+3\cdot0&0\cdot(-2)+3\cdot3\end{array}\right] =\left[\begin{array}{cc}1&-8\\0&9\end{array}\right]](https://tex.z-dn.net/?f=A%5E%7B2%7D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C0%263%5Cend%7Barray%7D%5Cright%5D%20%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C0%263%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%5Ccdot1-2%5Ccdot0%261%5Ccdot%28-2%29-2%5Ccdot3%5C%5C0%5Ccdot1%2B3%5Ccdot0%260%5Ccdot%28-2%29%2B3%5Ccdot3%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-8%5C%5C0%269%5Cend%7Barray%7D%5Cright%5D "A^{2}=\left[\begin{array}{cc}1&-2\\0&3\end{array}\right] \cdot\left[\begin{array}{cc}1&-2\\0&3\end{array}\right] =\left[\begin{array}{cc}1\cdot1-2\cdot0&1\cdot(-2)-2\cdot3\\0\cdot1+3\cdot0&0\cdot(-2)+3\cdot3\end{array}\right] =\left[\begin{array}{cc}1&-8\\0&9\end{array}\right]")
![A^{3}=\left[\begin{array}{cc}1&-2\\0&3\end{array}\right] \cdot\left[\begin{array}{cc}1&-2\\0&3\end{array}\right] \cdot\left[\begin{array}{cc}1&-2\\0&3\end{array}\right] =\left[\begin{array}{cc}1&-8\\0&9\end{array}\right] \cdot \left[\begin{array}{cc}1&-2\\0&3\end{array}\right] =\\\\ \left[\begin{array}{cc}1\cdot1-8\cdot0&1\cdot(-2)-8\cdot3\\0\cdot1+9\cdot0&0\cdot(-2)+9\cdot3\end{array}\right] =\left[\begin{array}{cc}1&-26\\0&27\end{array}\right]](https://tex.z-dn.net/?f=A%5E%7B3%7D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C0%263%5Cend%7Barray%7D%5Cright%5D%20%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C0%263%5Cend%7Barray%7D%5Cright%5D%20%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C0%263%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-8%5C%5C0%269%5Cend%7Barray%7D%5Cright%5D%20%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C0%263%5Cend%7Barray%7D%5Cright%5D%20%3D%5C%5C%5C%5C%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%5Ccdot1-8%5Ccdot0%261%5Ccdot%28-2%29-8%5Ccdot3%5C%5C0%5Ccdot1%2B9%5Ccdot0%260%5Ccdot%28-2%29%2B9%5Ccdot3%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-26%5C%5C0%2627%5Cend%7Barray%7D%5Cright%5D "A^{3}=\left[\begin{array}{cc}1&-2\\0&3\end{array}\right] \cdot\left[\begin{array}{cc}1&-2\\0&3\end{array}\right] \cdot\left[\begin{array}{cc}1&-2\\0&3\end{array}\right] =\left[\begin{array}{cc}1&-8\\0&9\end{array}\right] \cdot \left[\begin{array}{cc}1&-2\\0&3\end{array}\right] =\\\\ \left[\begin{array}{cc}1\cdot1-8\cdot0&1\cdot(-2)-8\cdot3\\0\cdot1+9\cdot0&0\cdot(-2)+9\cdot3\end{array}\right] =\left[\begin{array}{cc}1&-26\\0&27\end{array}\right]")
![f(A)=3\cdot A^3-2\cdot A+4\cdot E=3\cdot\left[\begin{array}{cc}1&-26\\0&27\end{array}\right] -2\cdot\left[\begin{array}{cc}1&-2\\0&3\end{array}\right]+4\cod\left[\begin{array}{cc}1&0\\0&1\end{array}\right]=\\\\ =\left[\begin{array}{cc}3\cdot1-2\cdot1+4\cdot1&3\cdot(-26)-2\cdot(-2)+4\cdot0\\3\cdot0-2\cdot0+4\cdot0&3\cdot27-2\cdot3+4\cdot1\end{array}\right]=\left[\begin{array}{cc}5&-74\\0&79\end{array}\right]](https://tex.z-dn.net/?f=f%28A%29%3D3%5Ccdot%20A%5E3-2%5Ccdot%20A%2B4%5Ccdot%20E%3D3%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-26%5C%5C0%2627%5Cend%7Barray%7D%5Cright%5D%20-2%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%26-2%5C%5C0%263%5Cend%7Barray%7D%5Cright%5D%2B4%5Ccod%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C0%261%5Cend%7Barray%7D%5Cright%5D%3D%5C%5C%5C%5C%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%5Ccdot1-2%5Ccdot1%2B4%5Ccdot1%263%5Ccdot%28-26%29-2%5Ccdot%28-2%29%2B4%5Ccdot0%5C%5C3%5Ccdot0-2%5Ccdot0%2B4%5Ccdot0%263%5Ccdot27-2%5Ccdot3%2B4%5Ccdot1%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D5%26-74%5C%5C0%2679%5Cend%7Barray%7D%5Cright%5D "f(A)=3\cdot A^3-2\cdot A+4\cdot E=3\cdot\left[\begin{array}{cc}1&-26\\0&27\end{array}\right] -2\cdot\left[\begin{array}{cc}1&-2\\0&3\end{array}\right]+4\cod\left[\begin{array}{cc}1&0\\0&1\end{array}\right]=\\\\ =\left[\begin{array}{cc}3\cdot1-2\cdot1+4\cdot1&3\cdot(-26)-2\cdot(-2)+4\cdot0\\3\cdot0-2\cdot0+4\cdot0&3\cdot27-2\cdot3+4\cdot1\end{array}\right]=\left[\begin{array}{cc}5&-74\\0&79\end{array}\right]")