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We have seen that under the standard basis, $$\hat { \imath } = \langle 1,0 \rangle$$ and $$\hat { \jmath } = \langle 0,1 \rangle$$ , that we can add the vectors $$\vec { u } = \langle a , b \rangle$$ and $$\vec { v } = \langle c , d \rangle$$ tip-to-tail. Show that tip-to-tail addition works for any pair of basis vectors $$( \hat { \imath }$$ and $$\hat { \jmath } )$$ , not just the standard basis.
$$u+ v= (a+ c,b+ d)$$