<s>[INST] Find the value of $x,y,z$ that minimize $3x^2+2y^2+z^2+4xy+4yz$ under constraint $x^2+y^2+z^2 = 1$ Find the value of $x,y,z$ that minimize $3x^2+2y^2+z^2+4xy+4yz$ under constraint $x^2+y^2+z^2 =  1 $
i am learning algebra and think a way solve this problem by matrix
 [/INST] by Lagrange Multiplier Method we get $$3x^2+2y^2+z^2+4xy+4yz\geq -1$$ and the equal sign holds if $$x=-\frac{1}{3},y=\frac{2}{3},z=-\frac{2}{3}$$
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