I have been really struggling to get my head around the following. Solve the equation 2((1,2,3)-X) - (-2,0,4) = -2(1,2,3) for X. Help appreciated.
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Let $\displaystyle X=(x,y,z)$. $\displaystyle 2[(1,2,3)-(x,y,z)]-(-2,0,4)=-2(1,2,3)$ $\displaystyle (2,4,6)-2(x,y,z)=(-2,0,4)-(2,4,6)$ $\displaystyle 2(x,y,z)=2(2,4,6)-(-2,0,4)=(6,8,8)\Rightarrow (x,y,z)=(3,4,4)$
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