I. If u, v and w are linearly independent then show that the set {u+v,u+w,v+w} is...

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I. If u, v and w are linearly independent then show that the set {u+v,u+w,v+w} is linearly independent set of vectors If a, b and c are distinct elements the show that II. {(1,1,1),(a,b,c).(a², b², c²)} forms basis for R³ III. p(x)=x²-x²+2x+3 q(x)=3x³+x²-x-1 r(x)=x³+2x+2 s(x)=7x³+ax²+5 For what value of a' the set {p.q, r,s} is linearly dependent I. If u, v and w are linearly independent then show that the set {u+v,u+w,v+w} is linearly independent set of vectors If a, b and c are distinct elements the show that II. {(1,1,1),(a,b,c).(a², b², c²)} forms basis for R³ III. p(x)=x²-x²+2x+3 q(x)=3x³+x²-x-1 r(x)=x³+2x+2 s(x)=7x³+ax²+5 For what value of a' the set {p.q, r,s} is linearly dependent