(a) Is the family 13 = (1, v2, /3) of the elements 1, v2, v3 € R in the Q-vector space R is linear and- dependent? If so, specify the subspace U of R, of which B is a base. What kind Does U have a dimension?

(b) Show that R as a vector space over Q has no finite dimension, i.e. dimg R = 00. (Note: Use the fact (without proof) that for k € N the two quantities Qk and R is not equal.)