Give an example of a linear transformation 7:r-r" such that t (v)= -v for all ve r (6) let v be a real n-dimensional vector space and let t:v~v be a linear tran

Give an example of a linear transformation 7:R-R" such that T (v)= -v for all ve R (6) Let V be a real n-dimensional vector space and let T:V~V be a linear transformation satisfying T (o) = -v for all ve V ) Show that n is even. Use T to make V into a complex vector space such that the multiplication by complex numbers extends the multiplication by real numbers. (l) Show that, with respect to the complex vector space structure on V obtained in (ii), T:V»V is a complex linear transformation (u) (9)