If three matrices A =[2 1 4 1], B =[3 4 2 3] and C =[3 -4 -2 3] . Then t r( A )+ t r (( ABC /2))+ t r(( A ( BC )2/4)) +tr((A(B C)3/8))+ ldots ∞=

Question

If three matrices A =[2 1 4 1], B =[3 4 2 3] and C =[3 -4 -2 3] . Then t r( A )+ t r (( ABC /2))+ t r(( A ( BC )2/4)) +tr((A(B C)3/8))+ ldots ∞= (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

BC =[3 4 2 3][3 -4 -2 3]=[1 0 0 1]= I t r ( A )+ t r (( ABC /2))+ t r (( A ( BC )2/4)) + t r (( A ( BC )3/8))+ ldots ldots+∞ = t r ( A )+ t r (( A /2))+ t r (( A /4))+ ldots ldots ∞ = t r ( A )+(1/2) t r ( A )+(1/22) t r ( A )+ ldots ldots ∞ =( t r ( A )/1-1 / 2)=2 t r ( A )=2(3)=6

Q. If three matrices A=[24​11​],B=[32​43​] and C=[3−2​−43​]. Then tr​(A)+tr​(2ABC​)+tr​(4A(BC)2​) +tr​(8A(BC)3​)+…∞=

BC=[32​43​][3−2​−43​]=[10​01​]=I tr​(A)+tr​(2ABC​)+tr​(4A(BC)2​) +tr​(8A(BC)3​)+……+∞ =tr​(A)+tr​(2A​)+tr​(4A​)+……∞ =tr​(A)+21​tr​(A)+221​tr​(A)+……∞ =1−1/2tr​(A)​=2tr​(A)=2(3)=6

Q. If three matrices $A = [2411], B = [3243]$ and $C = [3 - 2 - 4 3] .$ Then $t_{r} (A) + t_{r} (\frac{A BC}{2}) + t_{r} (\frac{A ( BC ) ^{2}}{4})$ $+ t_{r} (\frac{A ( BC ) ^{3}}{8}) + \dots \infty =$