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Algebra
Question

We have seen that under the standard basis, \( \ha...

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. 

Answer

\(u+ v= (a+ c,b+ d)\)

Solution
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