Let v1 = (4, 6, 7)T , v2 = (0, 1, 1)T , v3 = (0, 1, 2)T , and let u1, u2, and u3 be the vectors given in Exercise 5.
(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}.
Reference: Exercise 5:
Let u1 = (1, 1, 1)T , u2 = (1, 2, 2)T , u3 = (2, 3, 4)T .
(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}:
(i) (3, 2, 5)T (ii) (1, 1, 2)T (iii) (2, 3, 2)T
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