Problem 3 The linear operator A : R3 - R& is defined by: A(vi) = wi, where v1 = (1, 1, 1), v2 = (1, 2, 2), v3 = (1, 1, 2), w1 = (1, 1, 0, 0), w2 = (0, 1, 1, 0), w3 = (0, 0, 1, 1). Find the matrix A of A in the standard bases (1, 0, 0), *(0, 1, 0), *(0, 0, 1) of R3 and t (1, 0, 0, 0), (0, 1, 0, 0), (0, 0, 1, 0), (0, 0, 0, 1) of R. Remark. Here and below (X1, ...,Xn) denotes the transpose (i.e. the vector column) of the vector-row (X1, ..., Xn)