Даны две матрицы матриц A и B. Найдите: а) AB; б) BA. A=8 5 −1 B= 6 −7 −6

6 5 3 3 2 -1

1 3 5 7 8 2

Пошаговое объяснение:

A*B=C

c₁₁ = a₁₁*b₁₁ + a₁₂*b₂₁+ a₁₃*b₃₁ = 8*6 + 5 *3 + (-1)*7 = 48 + 15 - 7 = 56  

c₁₂ = a₁₁*b₁₂ + a₁₂*b₂₂ + a₁₃*b₃₂ = 8 *7 + 5 *2 + (-1) *8 = 56 + 10 - 8 = 58  

c₁₃ = a₁₁*b₁₃ + a₁₂*b₂₃+ a₁₃*b₃₃ = 8*(-6) + 5*(-1) + (-1)*2 = (-48) - 5 - 2 = -55  

c₂₁ = a₂₁*b₁₁ + a₂₂*b₂₁ + a₂₃*b₃₁ = 6*6 + 5*3 + 3*7 = 36 + 15 + 21 = 72  

c₂₂= a₂₁*b₁₂ + a₂₂*b₂₂ + a₂₃*b₃₂ = 6*7 + 5*2 + 3*8 = 42 + 10 + 24 = 76  

c₂₃ = a₂₁*b₁₃ + a₂₂*b₂₃ + a₂₃*b₃₃ = 6*(-6) + 5* (-1) + 3 *2 = (-36) - 5 + 6 = -35  

c₃₁ = a₃₁*b₁₁ + a₃₂*b₂₁ + a₃₃*b₃₁ = 7*6 + 3*3 + 5*7 = 42 + 9 + 35 = 86  

c₃₂ = a₃₁*b₁₂ + a₃₂*b₂₂ + a₃₃*b₃₂ = 7*7 + 3*2 + 5*8 = 49 + 6 + 40 = 95  

c₃₃ = a₃₁ *b₁₃ + a₃₂*b₂₃ + a₃₃*b₃₃ = 7*(-6) + 3*(-1) + 5*2 = (-42) - 3 + 10 = -35

      56   58   -55

C=  72   76   -35

       86   95   -35

ВА=C₁   считается аналогично

c₁₁ = 6 *8 + (-7)*6 + (-6)*1 = 48 - 42 - 6 = 0

c₁₂ = 6*5 + (-7)*5 + (-6)*3 = 30 - 35 - 18 = -23

c₁₃ = 6*(-1) + (-7)*3 + (-6)*5 = (-6) - 21 - 30 = -57

c₂₁ = 3*8 + 2*6 + (-1)*1 = 24 + 12 - 1 = 35

c₂₂ = 3*5 + 2*5 + (-1)* 3 = 15 + 10 - 3 = 22

c₂₃ =  3*(-1) + 2*3 + (-1)*5 = (-3) + 6 - 5 = -2

c₃₁ = 7 *8 + 8 *6 + 2*1 = 56 + 48 + 2 = 106

c₃₂ =  7* 5 + 8*5 + 2*3 = 35 + 40 + 6 = 81

c₃₃ = 7*(-1) + 8*3 + 2 *5 = (-7) + 24 + 10 = 27

       0   -23    -57

С₁=  35   22    -2

      106   81     27

111

102

201

120

210

300