Question: Please use R programming to answer below questions. 1. Create the following matrices: l 2 3 4 4 3 2 l 4 3 2 1

Please use R programming to answer below questions.

1. Create the following matrices: l 2 3 4 4 3 2 l 4 3 2 1 5 6 7 3 3 6 4 2 5 6 ? 8 9 10 ll 12 2 4 6 3 8 7 6 5 13 14 15 16 1 2 3 4 4 3 2 1 Define tr(X) (stands for trace of X) as the sum of all the diagonal elements of X. For example, tr(A)=34, tr(B)=20 and tr(C)=17. Verify the following: a. tr(ABC) = tr(CAB) = tr(BCA) b. (ABC)' = C'B'A' (Note: A' is transpose of A) c. (DB)_1 =.B_1D_1 where D = | + A

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