Question

Simplify the following indicial expressions as much as possible. ΣΣ1C,B (a) Substitute Cii = -1 AipBpj into a = k 1 Hint: Consider changing the index j to index k in the expression for C;i 3 ( b) Σ-Σ_ Σ1 Α, Βιδικ - Σ Σ Σ-12AB , im rį=1 i=1 m=1 Hint: Use the index substitution property of Kronecker delta first to simplify the expression. When you do that, the triple summation will reduce to double summation in each symbol group.

Answer 1

Cik Bin TT R=1 ut Cij = Aip Bei pa Change to k Cir 1 ip Lрд we Ci Bi, t (iz Bizt (iz Biz 25C., B., t Car Bar + G, Bo ] + С Д + С. Дәз + су Ту, & Cs Big & Caz Dagt C Bog)

p-t > 2=TArp bor) bor + ( <Aplon Bar + ({ Agro) Bs, + 2 Alp Bp 2 / B2 + ( 3 App D22) Bog pat Pa) t =1 +/{ Asp Boz) Daz +1 (Ardpy) Bot (? App Des) 35 7 { Ap Bp3 B / - A B & A 12 B21 But Als By, Bu + Ag, Bi. Bgi + Azz Bg, + Azz By, B2, + Aj B B + A22 Ba Ba & Az, B2 + A, B + A12 Bg 2 B12 + AD B22 B12 + Ag, B12 Dag + A22 Biz & Ag, B22 Baz + A Diz Diz + A22 B 22 Dy + A B 2 + A2 B 2 + AIR Dg Dist Ag By Di + Adi Di2 Dag & Adg D aj + A2, B2, D2 +AJ BODD + A22 B23 Dg of Az D7

Date Page ? ? { Aig Bip dir - {2 Aim Bunkedik i=1 7-1 R =1 ial makal Ai, B , dilt Big dia + Bij diz] 19171 [a Ain Dmidi, & Bonadiz 11 mai А, 3, 4А, 22, + A, D.] dia ( Air B12 + Aig Bag & Ain D22] S A By + A2 O2 + A,5 15, , + E Sil [2 Ai, Birta Aid Bg , + 2 Air B T 3 Sig 2 Ai, B12 +2 Air Dog to Ais B, ia & Siz [ & Ai, Bryta Air B2, +2 Ai sf)

= A , + А, Д, + Ais 35 + А., П., 4 А,, дәә + A5, 23, + А, , + Ауа да + Аз Дуу 2А, 3 - 2 А, 2. Зо, - 2 А, В, 2 А2, 3,2 - 2 А, , , - 2 А2, 3, 4 — ЭА), В.) - 245, - 2А5, 2, 2. А ) - А, 12, - А., 1, — А, В, - А., В, - А., 1) - – А5, 22 - А5, ) - А) В)) -- AI D + A12B1 + ADBI 4 А, D, + A), О,9 + 4) 22 2 t As, Dia + A12 D2) + A3) B ]