A find the transition matrix corresponding to the change of

Question

Problem 1: Let U₁ = (1, 1. 1)^r , u2 = (2, 3, 4)^r.

(a) Find the transition matrix corresponding to the change of basis from [e₁, e₂, e₃] to [u₁, u₂, u₃].

(b) Find the coordinates of each of the following vectors with respect to [u₁, u₂, u₃].

Problem 2: Let = (4, 6, 7)^r, v₂ = (0, 1, 1)^r, v₃ = (0, 1, 2)^r, and let u₁, u₂, u₃ be the vectors.

(a) Find the transition matrix from [v1, v2, v3] to [u1, u2, u3].

(b) If x = 2v1 + 3v2 - 4v3, determine the coordinates of x with respect to [u1, u2, u3].