1. Consider R³ with the usual addition + of vectors, but with scalar multiplication O defined by ko y ky | 2kz] y ER³. %3D Show that R³ together with the operations + and © is not vector space. 1 2....

1. Consider R³
with the usual addition of vectors, but with scalar multiplication defined by the attached image. Show that R³
togather with the operations addition and scalar multiplication is not vector space.

2. Let u= (attached image) and v= (attached image) be two vectors in R³. Consider the subset W = {au + bv : a, b is inside R},

of R³. Show that W is a subspace of R³.

Extracted text: 1. Consider R³ with the usual addition + of vectors, but with scalar multiplication O defined by ko y ky | 2kz] y ER³. %3D Show that R³ together with the operations + and © is not vector space. 1 2. Let u = and v = 3 be two vectors in R³. Consider the subset W = {au+bv : a, b e R}, of R³. Show that W is a subspace of R³.