Mathematics, 01.04.2020 19:30 janae789
Fit a quadratic function of the form ()=c0+c1+c22f(t)=c0+c1t+c2t2 to the data points (0,10)(0,10), (1,6)(1,6), (2,26)(2,26), (3,30)(3,30), using least squares.
Answers: 2
![A=\left[\begin{array}{ccc}1&0&0\\1&1&1\\1&2&4\\1&3&9\end{array}\right]](/tpl/images/0575/9043/6b69e.png)
, ![\vec x= \left[\begin{array}{c}c_0\\c_1\\c_2\end{array}\right]](/tpl/images/0575/9043/9e15c.png)
and ![\vec b=\left[\begin{array}{ccc}10\\16\\26\\30\end{array}\right]](/tpl/images/0575/9043/91655.png)
![\left[\begin{array}{c}c_0\\c_1\\c_2\end{array}\right]=\left(\left[\begin{array}{cccc}1&1&1&1\\0&1&2&3\\0&1&4&9\end{array}\right] \left[\begin{array}{ccc}1&0&0\\1&1&1\\1&2&4\\1&3&9\end{array}\right]\right)^{-1}\left[\begin{array}{cccc}1&1&1&1\\0&1&2&3\\0&1&4&9\end{array}\right]\left[\begin{array}{ccc}10\\16\\26\\30\end{array}\right]](/tpl/images/0575/9043/8c67c.png)
![\left[\begin{array}{c}c_0\\c_1\\c_2\end{array}\right]=\left(\left[\begin{array}{ccc}4&6&14\\6&14&36\\14&36&98\end{array}\right] \right)^{-1}\left[\begin{array}{cccc}1&1&1&1\\0&1&2&3\\0&1&4&9\end{array}\right] \left[\begin{array}{ccc}10\\16\\26\\30\end{array}\right]](/tpl/images/0575/9043/76b9d.png)
![\left[\begin{array}{c}c_0\\c_1\\c_2\end{array}\right]=\left[\begin{array}{ccc}\frac{19}{20}&-\frac{21}{20}&\frac14 \\ \\-\frac{21}{20}&\frac{49}{20}&-\frac{3}{4}\\ \\ \frac14&-\frac34& \frac14 \end{array}\right] \left[\begin{array}{cccc}1&1&1&1\\0&1&2&3\\0&1&4&9\end{array}\right] \left[\begin{array}{ccc}10\\16\\26\\30\end{array}\right]](/tpl/images/0575/9043/86843.png)
![\left[\begin{array}{c}c_0\\c_1\\c_2\end{array}\right]= \left[\begin{array}{c}\frac{19}{2}\\ \\\frac{17}{2}\\ \\-\frac12\end{array}\right]](/tpl/images/0575/9043/8756a.png)
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Fit a quadratic function of the form ()=c0+c1+c22f(t)=c0+c1t+c2t2 to the data points (0,10)(0,10), (...
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