P4. Prove: If V = {V1, V2, ...,V) is a linearly indepen- dent set of vectors...

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P4. Prove: If V = {V1, V2, ...,V) is a linearly indepen- dent set of vectors in R, and if W = {Wx+1, ...,wn} is a basis for

VUW = {V1, V2, ..., Vk, Wk+1,...,w.} is a basis for R. [Hint: Since V UW contains n vectors, it suffices to show that VUW is

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/ linearly independent ta solution, 40, (2) e} is set of vectores in IR. Wapoker, ...., an}. is a basis for the nell space o Now fruce Thence aim (Im LA) ak; LA (WW)} is cineany Insefladent, 4,7) 2 :. 4 = C2 =- CK From ♡ we get , it cu un Cuti -- wn

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