Consider the vector space R 2 where vector addition and scalar multiplication are defined in the usual way. Also consider the ordered basis

E={el,s={(3)a(:')} of R2, the ordered set of vectors M={,fa}={,(3}Ci and the vector v = G) E R2. (a) Show that M is a basis of 13.2. (b) 1Write down the coordinate vector [VJE of v and the transition matrix P M from M-coordinates to E-coordinates and hence use the fact that W E R2, (u = P(v)g to nd (V)M. (c) On a single graph, sketch the vector v and show how to obtain it (i) as a linear combination of the E-basis vectors and (ii) 33 a linear combination of the M-basis vectors