Which vector spaces are isomorphic to R6?(a) M2,3 (b) P6 (c) C[0, 6](d) M6,1 (e) P5 (f) C′[−3, 3](g) {(x1, x2, x3, 0, x5, x6, x7): xi is a real number}

Use the function to find the image of v and the preimage of w. T(V3, V2) = ( V2, V1 + V2, 2v1 - V2 2 v = (2, 2), w = (-6/2, 0, -18) (a) the image of v (0,4,2) (b) the preimage of w (If the vector has an infinite number of solutions, give your answer in terms of the parameter t.) (2,36)

"On R², define the operations of addition and scalar multiplication as follows: (X₁, X₂) + (y₁ Y₂) = (x₂ + y₂ +1, x₂ + y₂ + 1), c(x₁, x₂) = (Cx₂ + C-1, ₂+c-1). Then R² with these operations forms a vector space." Note that here the zero vector is (-1,-1) and the additive inverse of (x1, x2) is (-X₁-2, -x₂-2), not (-x₂-x₂)- a) Show that (-1, -1) acts as the zero vector under these definitions.