File Preview\ (I) Consider

R^(3)

with the usual inner product,

(:x,y:)=x^(T)y

. Let

x_(1)=[[1],[2],[3]],x_(2)=[[1],[-2],[3]],x_(3)=[[0],[1],[1]]

.\ (i) Show that

{x_(1),x_(2),x_(3)}

is a linearly independent set.\ (ii) Generate an orthonomal set using Gram-Schmidt procedure.\ (iii) Express the vector

z=[[6],[4],[-3]]

in terms of the basis generated in part (ii).

ile Preview (1) Consider R3 with the usual inner product, x,y=xTy. Let x1=123,x2=123,x3=011. (i) Show that {x1,x2,x3} is a linearly independent set. (ii) Generate an orthonomal set using Gram-Schmidt procedure. (iii) Express the vector z=643 in terms of the basis generated in part (ii)