Question: 12.5. (Sec. 12.2) Let AI;;:>: A2;;:>: ... ;;:>: Aq > 0 be the positive roots of (14), where 111 and 122 are q X q

12.5. (Sec. 12.2) Let AI;;:>: A2;;:>: ... ;;:>: Aq > 0 be the positive roots of (14), where 111 and 122 are q X q nonsingular matrices.

(a) What is the rank of I12?

(b) Write ni_IA~ as the determinant of a rational function of III' 1 12 , 1 21 , and 1 22, Justify your answer.

(c) If Aq = I, what is the rank of

W 22

W 22

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