Let a : V → W be a linear map for vector spaces V, W over R, V₁, V2, V3, V4 a basis of V and w₁, W2, W3 a basis of W. Suppose that the corresponding matrix 0 2 -1 0 with respect to these bases is A = 1 0 -1 −1 0 3 0 3

Let B = {b, b, b3} be a basis for vector space V. Let T: V → V be a linear transformation with the following properties. T(b,) = - 8b, - 6b2: T(b2) = - 2b, +4b2: T(b3) = - 7b, %3D Find [T]B, the matrix for T relative to B.

Let B = {b₁,b2,b3} be a basis for vector space V. Let T: V → V be a linear transformation with the following properties. == T(b₁) = -6b₁ + 5b₂, T(b₂) -3b₁ +4b₂, T (b3) =b₁ 1 Find [T]B, the matrix for T relative to B.

B = (v1, v2, V3) is a basis of the vector space V and T :V →V is a linear transformation which satisfies T(vı) = v1 + v2 + 2v3, T(v2) = 2v1 + v2 + 3v3, T(v3) = vị + 2v2 + 3v3. If v = vị – v2 + 2v3 then T(v) = a) vi + 4v2 + 5v3 b) vị – v2 + 2v3 c) 6v1 + 6v2 + 9v3 d) 4v1 + 7v2 +5v3 e) 5v1 + 6v2 + 1lv3