Given a positive integer n, let a2,n a2,n–1 a3,n–2 a3,n–1 a3,n An = An-1,n аn-1,2 ап-1,n-2 аn-1,л-1 ... An,n-2 An,n-1 An,n An,1 An,2 whose a¡j entries with i+j < n are all equal to 0. Conjecture a formula for det(An) and prove it.

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A: The cube root of unity is written as:

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Q: Given a positive integer n, let a2,n–1 a2,n a3,n-2 a3,n-1 a3,n An = аn-1,2 аn-1,n-2 аn-1,п-1 @n-1,п…

A: Given: Here the given positive integer n, Let An = 00...00a1,n00...0a2,…

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A: Solution is given below:

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Q: A cosets of of 212 are اخترأحد الخیارات + 2, +1,.1 O + 1,.2 O + 4, + 1, .3 + 4, + 2, + 1 , .4 O

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A: Find change all inequality to grater then equal to 0. Then use the theorem

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Q: ne order of the element 16+ in Z24/ is None of the choices 8.

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Q: let s be positive integer, then (2) + (;) = %3D

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Q: hen Let here a11 = , 923 = , 912 = " A = A-¹ a31 = = 1 1 all a21 a31 8 8 -8 , a13 = a12 a22 a32 " 0…

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Q: Let A, BeM,(C). Prove that for every integer k21, tr(AB) =tr(BA) Does tr(AB) =tr(A*B* )? Explain…

A: We will do both these subparts of this question for you. Solving this question requires basic…