![G$iven A=\left[\begin{array}{ccc}3&2&0\\2&2&1\\0&1&0\end{array}\right]](/tpl/images/0686/9367/1d9b0.png)
for A.![x=\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right]](/tpl/images/0686/9367/ab99d.png)
![x^TAx = \left[\begin{array}{ccc}x_1&x_2&x_3\end{array}\right]\left[\begin{array}{ccc}3&2&0\\2&2&1\\0&1&0\end{array}\right]\left[\begin{array}{ccc}x_1\\x_2\\x_3\end{array}\right]](/tpl/images/0686/9367/0a013.png)
![= \left[\begin{array}{ccc}x_1&x_2&x_3\end{array}\right]\left[\begin{array}{ccc}3x_1+2x_2+0x_3\\2x_1+2x_2+1x_3\\0x_1+1x_2+0x_3\end{array}\right]](/tpl/images/0686/9367/b6431.png)
![x=\left[\begin{array}{ccc}-2\\-1\\5\end{array}\right]\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\\=3(-2)^2+4(-2)(-1)+2(-1)^2+2(-1)(5)\\=3*4+4*2+2-10\\=12+8+2-10\\=12](/tpl/images/0686/9367/dbe32.png)
![x=\left[\begin{array}{ccc}\frac{1}{2}\\\frac{1}{2}\\\frac{1}{2}\end{array}\right]\\x^TAx=3x_1^2+4x_1x_2+2x_2^2+2x_2x_3\\=3(\frac{1}{2})^2+4(\frac{1}{2})(\frac{1}{2})+2(\frac{1}{2})^2+2(\frac{1}{2})(\frac{1}{2})\\\\=\frac{3}{4}+1+ \frac{1}{2}+\frac{1}{2}\\\\=2\frac{3}{4}](/tpl/images/0686/9367/56171.png)
Compute the quadratic form xTAx for A = [3 2 0, 2 2 1, 0 1 0].
A. x = [x1 x2 x3].
B. x = [-2...
Mathematics, 16.06.2020 16:57 jessnolonger
Compute the quadratic form xTAx for A = [3 2 0, 2 2 1, 0 1 0].
A. x = [x1 x2 x3].
B. x = [-2 -1 5].
C. x = [1/2 1/2 1/2].
Answers: 1
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