3. Problem 3: Let V be the collection of vectors of the form [ positive real numbers; vector addition and scalar multiplication in V are defined as: b where a and b are by] and co[a b] = [ a° b° ] For example, [ 2 4] [ 5 1/2] = [ 10 2] and 3 0 [ 2 4 ] = [ 8 64 ]. Using u = [a b] and v = [ x vector space properties for V. y], prove that V is a vector space by verifying all 10

Given x₁ = [¹¹]¹, x₂ = [1 -1 1]], *₂ = [1 [1 basis vectors. Assume that {xi} form. The a 121,3 0 0]] Find reciprocal basic vectors. Express the vector Y = {6 3 1] in terms of these basis vectors.