All bases considered in these are assumed to be ordered bases.

Daniaal Sanchez 2021-02-21 Answered

All bases considered in these are assumed to be ordered bases. In Exercise, compute the coordinate vector of v with respect to the giving basis S for V. V is R2,S={[10][01]},v=[32]

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2k1enyvp
Answered 2021-02-22 Author has 94 answers

We are given the following ordered basis S for the vector space V=R2as well as the following vector v in V: S={[10][01]};v=[32] We have to compute the coordinate vector [v]_s of v with respect to the basis S. We have [v]s=[ab] Where v=[32]
=a[10]+b[01]
=[ab] Equating components yields the following linear system: a=3andb=2 Threfore, the coordinate vector [v]S of v with respect to the basis S is [v]S=[32]

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