Ответ:
110
Пошаговое объяснение:
Перемножим матрицы A*C=
Подробно как считать каждый элемент:
ac11 = a11 · c11 + a12 · c21 + a13 · c31 = (-2) · (-2) + (-3) · 2 + 1 · (-3) = 4 - 6 - 3 = -5
ac12 = a11 · c12 + a12 · c22 + a13 · c32 = (-2) · (-4) + (-3) · (-1) + 1 · 2 = 8 + 3 + 2 = 13
ac13 = a11 · c13 + a12 · c23 + a13 · c33 = (-2) · 3 + (-3) · 3 + 1 · 2 = (-6) - 9 + 2 = -13
ac21 = a21 · c11 + a22 · c21 + a23 · c31 = (-1) · (-2) + 2 · 2 + (-4) · (-3) = 2 + 4 + 12 = 18
ac22 = a21 · c12 + a22 · c22 + a23 · c32 = (-1) · (-4) + 2 · (-1) + (-4) · 2 = 4 - 2 - 8 = -6
ac23 = a21 · c13 + a22 · c23 + a23 · c33 = (-1) · 3 + 2 · 3 + (-4) · 2 = (-3) + 6 - 8 = -5
λAC=
Перемножим матрицы B*C=
bc11 = b11 · c11 + b12 · c21 + b13 · c31 = 1 · (-2) + (-2) · 2 + (-3) · (-3) = (-2) - 4 + 9 = 3
bc12 = b11 · c12 + b12 · c22 + b13 · c32 = 1 · (-4) + (-2) · (-1) + (-3) · 2 = (-4) + 2 - 6 = -8
bc13 = b11 · c13 + b12 · c23 + b13 · c33 = 1 · 3 + (-2) · 3 + (-3) · 2 = 3 - 6 - 6 = -9
bc21 = b21 · c11 + b22 · c21 + b23 · c31 = 4 · (-2) + (-3) · 2 + (-5) · (-3) = (-8) - 6 + 15 = 1
bc22 = b21 · c12 + b22 · c22 + b23 · c32 = 4 · (-4) + (-3) · (-1) + (-5) · 2 = (-16) + 3 - 10 = -23
bc23 = b21 · c13 + b22 · c23 + b23 · c33 = 4 · 3 + (-3) · 3 + (-5) · 2 = 12 - 9 - 10 = -7
μBC=
складываем поэлементно D=λAC+μBC=
D22=110
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Answers & Comments
Ответ:
110
Пошаговое объяснение:
Перемножим матрицы A*C=![\left[\begin{array}{ccc}-5&13&-13\\18&-6&-5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%2613%26-13%5C%5C18%26-6%26-5%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{ccc}-5&13&-13\\18&-6&-5\end{array}\right]")
Подробно как считать каждый элемент:
ac11 = a11 · c11 + a12 · c21 + a13 · c31 = (-2) · (-2) + (-3) · 2 + 1 · (-3) = 4 - 6 - 3 = -5
ac12 = a11 · c12 + a12 · c22 + a13 · c32 = (-2) · (-4) + (-3) · (-1) + 1 · 2 = 8 + 3 + 2 = 13
ac13 = a11 · c13 + a12 · c23 + a13 · c33 = (-2) · 3 + (-3) · 3 + 1 · 2 = (-6) - 9 + 2 = -13
ac21 = a21 · c11 + a22 · c21 + a23 · c31 = (-1) · (-2) + 2 · 2 + (-4) · (-3) = 2 + 4 + 12 = 18
ac22 = a21 · c12 + a22 · c22 + a23 · c32 = (-1) · (-4) + 2 · (-1) + (-4) · 2 = 4 - 2 - 8 = -6
ac23 = a21 · c13 + a22 · c23 + a23 · c33 = (-1) · 3 + 2 · 3 + (-4) · 2 = (-3) + 6 - 8 = -5
λAC=![\left[\begin{array}{ccc}-5*(-3)&13*(-3)&-13*(-3)\\18*(-3)&-6*(-3)&-5*(-3)\end{array}\right] = \left[\begin{array}{ccc}15&-39&-39\\-54&18&15\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-5%2A%28-3%29%2613%2A%28-3%29%26-13%2A%28-3%29%5C%5C18%2A%28-3%29%26-6%2A%28-3%29%26-5%2A%28-3%29%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D15%26-39%26-39%5C%5C-54%2618%2615%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{ccc}-5*(-3)&13*(-3)&-13*(-3)\\18*(-3)&-6*(-3)&-5*(-3)\end{array}\right] = \left[\begin{array}{ccc}15&-39&-39\\-54&18&15\end{array}\right]")
Перемножим матрицы B*C=![\left[\begin{array}{ccc}3&-8&-9\\1&-23&-7\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26-8%26-9%5C%5C1%26-23%26-7%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{ccc}3&-8&-9\\1&-23&-7\end{array}\right]")
Подробно как считать каждый элемент:
bc11 = b11 · c11 + b12 · c21 + b13 · c31 = 1 · (-2) + (-2) · 2 + (-3) · (-3) = (-2) - 4 + 9 = 3
bc12 = b11 · c12 + b12 · c22 + b13 · c32 = 1 · (-4) + (-2) · (-1) + (-3) · 2 = (-4) + 2 - 6 = -8
bc13 = b11 · c13 + b12 · c23 + b13 · c33 = 1 · 3 + (-2) · 3 + (-3) · 2 = 3 - 6 - 6 = -9
bc21 = b21 · c11 + b22 · c21 + b23 · c31 = 4 · (-2) + (-3) · 2 + (-5) · (-3) = (-8) - 6 + 15 = 1
bc22 = b21 · c12 + b22 · c22 + b23 · c32 = 4 · (-4) + (-3) · (-1) + (-5) · 2 = (-16) + 3 - 10 = -23
bc23 = b21 · c13 + b22 · c23 + b23 · c33 = 4 · 3 + (-3) · 3 + (-5) · 2 = 12 - 9 - 10 = -7
μBC=![\left[\begin{array}{ccc}3*(-4)&-8*(-4)&-9*(-4)\\1*(-4)&-23*(-4)&-7*(-4)\end{array}\right] = \left[\begin{array}{ccc}-12&32&36\\-4&92&28\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%2A%28-4%29%26-8%2A%28-4%29%26-9%2A%28-4%29%5C%5C1%2A%28-4%29%26-23%2A%28-4%29%26-7%2A%28-4%29%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-12%2632%2636%5C%5C-4%2692%2628%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{ccc}3*(-4)&-8*(-4)&-9*(-4)\\1*(-4)&-23*(-4)&-7*(-4)\end{array}\right] = \left[\begin{array}{ccc}-12&32&36\\-4&92&28\end{array}\right]")
складываем поэлементно D=λAC+μBC=![\left[\begin{array}{ccc}15&-39&-39\\-54&18&15\end{array}\right]+\left[\begin{array}{ccc}-12&32&36\\-4&92&28\end{array}\right]=\left[\begin{array}{ccc}3&-7&-3\\-58&110&43\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D15%26-39%26-39%5C%5C-54%2618%2615%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-12%2632%2636%5C%5C-4%2692%2628%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26-7%26-3%5C%5C-58%26110%2643%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{ccc}15&-39&-39\\-54&18&15\end{array}\right]+\left[\begin{array}{ccc}-12&32&36\\-4&92&28\end{array}\right]=\left[\begin{array}{ccc}3&-7&-3\\-58&110&43\end{array}\right]")
D22=110