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IMG_0005 - ,r,^xS ri(il 6 r(ft rS\t r 6 r,aS =6 => r =!r=...

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309 Quiz 5.2 Name: Section number: (1) f4pts] Let V be a vector space and {rt,. .., vr} C V afinite set of vectorsin V. Give the definition for the set of vectors {tt,.. .,vn} to be iinearly independent. fI c,i, + ... *nil = O *r q = ..' =fir=C) ls{ha odU solution (2) [6pts] Let V be a vector spaceand {u, v, w} a set of lirreariy independent vectors in I/. Shorv that the set {v - u, v * w, u + 2w} is linearly independent.
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Unformatted text preview: ,r;, ( ,^xS ri (il 6\+ r.(ft rS\t r.( 6 * r,aS\ =6 => r, = !r= cs = O \ trx. knoa> c,d + c1i+csCj = o =) cr *c1=(3.= (r Tqvz r,(i- 3\+ qr(i+6)* t(6+e.6\=o Gr,+r)U + (c,+Af +(r"1ar)i3.e =) (r,*A=O-) cl*ra=e \bl. {d,il, d.,} ere L.I. car2q=6 J ;J* l!: l =) lio ind. \r? Lor o) ? [-t o n I r l ol-> Lc) r AJ-\ f t o ' lo I Loo...
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