I understand how the covariant frame we make from the contravariant frame of reference. I also understand that we can not write the position vector as I mentioned in the picture: $$\vec{r} = x_1 a_1 + x_2 a_2 \;.$$ I understand that I can not write in the above way because the resultant will be different. To make the resultant invariant we can write $$\vec{r} = x_1 a^1 + x_2 a^2\;.$$ But why covariant and contravariant are going together? Like why $x_1a^1$?
