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Question Number 202762 by Mastermind last updated on 02/Jan/24

Answered by shunmisaki007 last updated on 03/Jan/24

A= [(3,0,0),(0,3,0),(0,0,3) ] adj(A)= [( determinant ((3,0),(0,3)), determinant ((0,0),(0,3)), determinant ((0,0),(3,0))),( determinant ((0,0),(0,3)), determinant ((3,0),(0,3)), determinant ((3,0),(0,0))),( determinant ((0,3),(0,0)), determinant ((3,0),(0,0)), determinant ((3,0),(0,3))) ]= [(9,0,0),(0,9,0),(0,0,9) ] adj(adj(A))= [( determinant ((9,0),(0,9)), determinant ((0,0),(0,9)), determinant ((0,0),(9,0))),( determinant ((0,0),(0,9)), determinant ((9,0),(0,9)), determinant ((9,0),(0,0))),( determinant ((0,9),(0,0)), determinant ((9,0),(0,0)), determinant ((9,0),(0,9))) ]= [((27),0,0),(0,(27),0),(0,0,(27)) ] det(adj(adj(A)))= determinant (((27),0,0),(0,(27),0),(0,( 0),(27)))=19,683 ((det(adj(adj(A))))/5)=((19,683)/5)=3,936(3/5) ∴ {((det(adj(adj(A))))/5)}=(3/5) ★

A=[300030003]adj(A)=[|3003||0003||0030||0003||3003||3000||0300||3000||3003|]=[900090009]adj(adj(A))=[|9009||0009||0090||0009||9009||9000||0900||9000||9009|]=[270002700027]det(adj(adj(A)))=|270002700027|=19,683det(adj(adj(A)))5=19,6835=3,93635∴{det(adj(adj(A)))5}=35★

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