Repeat Exercise 51 for the case of five weighings of four objects and the following design matrices.

a.

b.

c.

Data from in  Exercise 51

Recall from the introductory section that the larger the determinant of D^TD, where D is the design matrix, the better will be the accuracy of the calculated weights for small light objects. Which of the following matrices corresponds to the best design for four weighings of four objects? Describe which of the objects S₁, S₂, S₃, and S₄ you would put in the left and right pans for each weighing corresponding to the best design matrix.

Transcribed Image Text:

D = 1 -1 1 1 ㅜㅜ 1 -1 1 1 1 1 -1 1