São dadas as matrizes A= [2 1][3 1] e B [3 4][1 0]
a) calcule AxB
b) calcule BxA
c) calcule A²
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Olá
A multiplicação de matrizes é feito através de linhas por colunas
A)
![A \left[\begin{array}{ccc}2&1\\3&1\\\end{array}\right]\cdot B \left[\begin{array}{ccc}3&4\\1&0\\\end{array}\right] \\ \\ \\ A\cdot B= \left[\begin{array}{ccc}((2\cdot3)+(1\cdot1))~~~~&((2\cdot4)+(1\cdot0))\\((3\cdot3)+(1\cdot1))~~~~&((3\cdot4)+(1\cdot0))\\\end{array}\right] \\ \\ \\ A\cdot B= \left[\begin{array}{ccc}(6+1)~~~~&(8+0)\\(9+1)~~~~&(12+0)\\\end{array}\right] \\ \\ \\ \boxed{\boxed{A\cdot B= \left[\begin{array}{ccc}7&8\\10&12\\\end{array}\right]}}](https://tex.z-dn.net/?f=A+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26amp%3B1%5C%5C3%26amp%3B1%5C%5C%5Cend%7Barray%7D%5Cright%5D%5Ccdot++B+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26amp%3B4%5C%5C1%26amp%3B0%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C++%5C%5C++%5C%5C+A%5Ccdot+B%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%28%282%5Ccdot3%29%2B%281%5Ccdot1%29%29%7E%7E%7E%7E%26amp%3B%28%282%5Ccdot4%29%2B%281%5Ccdot0%29%29%5C%5C%28%283%5Ccdot3%29%2B%281%5Ccdot1%29%29%7E%7E%7E%7E%26amp%3B%28%283%5Ccdot4%29%2B%281%5Ccdot0%29%29%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C++%5C%5C++%5C%5C+A%5Ccdot+B%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%286%2B1%29%7E%7E%7E%7E%26amp%3B%288%2B0%29%5C%5C%289%2B1%29%7E%7E%7E%7E%26amp%3B%2812%2B0%29%5C%5C%5Cend%7Barray%7D%5Cright%5D++%5C%5C++%5C%5C++%5C%5C+%5Cboxed%7B%5Cboxed%7BA%5Ccdot+B%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%26amp%3B8%5C%5C10%26amp%3B12%5C%5C%5Cend%7Barray%7D%5Cright%5D%7D%7D "A \left[\begin{array}{ccc}2&1\\3&1\\\end{array}\right]\cdot B \left[\begin{array}{ccc}3&4\\1&0\\\end{array}\right] \\ \\ \\ A\cdot B= \left[\begin{array}{ccc}((2\cdot3)+(1\cdot1))~~~~&((2\cdot4)+(1\cdot0))\\((3\cdot3)+(1\cdot1))~~~~&((3\cdot4)+(1\cdot0))\\\end{array}\right] \\ \\ \\ A\cdot B= \left[\begin{array}{ccc}(6+1)~~~~&(8+0)\\(9+1)~~~~&(12+0)\\\end{array}\right] \\ \\ \\ \boxed{\boxed{A\cdot B= \left[\begin{array}{ccc}7&8\\10&12\\\end{array}\right]}}")
B)
![B \left[\begin{array}{ccc}3&4\\1&0\\\end{array}\right] \cdot A \left[\begin{array}{ccc}2&1\\3&1\\\end{array}\right] \\ \\ \\ B\cdot A= \left[\begin{array}{ccc}((3\cdot2)+(4\cdot3))~~~~&((3\cdot1)+(4\cdot1))\\((1\cdot2)+(0\cdot3))~~~~&((1\cdot1)+(0\cdot1))\\\end{array}\right] \\ \\ \\ B\cdot A= \left[\begin{array}{ccc}(6+12)~~~~&(3+4)\\(2+0)~~~~&(1+0)\\\end{array}\right] \\ \\ \\ \boxed{\boxed{B\cdot A= \left[\begin{array}{ccc}18&7\\2&1\\\end{array}\right]}}](https://tex.z-dn.net/?f=B+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D3%26amp%3B4%5C%5C1%26amp%3B0%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5Ccdot+A+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26amp%3B1%5C%5C3%26amp%3B1%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%5C%5C+%5C%5C+B%5Ccdot+A%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%28%283%5Ccdot2%29%2B%284%5Ccdot3%29%29%7E%7E%7E%7E%26amp%3B%28%283%5Ccdot1%29%2B%284%5Ccdot1%29%29%5C%5C%28%281%5Ccdot2%29%2B%280%5Ccdot3%29%29%7E%7E%7E%7E%26amp%3B%28%281%5Ccdot1%29%2B%280%5Ccdot1%29%29%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%5C%5C+%5C%5C+B%5Ccdot+A%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%286%2B12%29%7E%7E%7E%7E%26amp%3B%283%2B4%29%5C%5C%282%2B0%29%7E%7E%7E%7E%26amp%3B%281%2B0%29%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%5C%5C+%5C%5C+%5Cboxed%7B%5Cboxed%7BB%5Ccdot+A%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D18%26amp%3B7%5C%5C2%26amp%3B1%5C%5C%5Cend%7Barray%7D%5Cright%5D%7D%7D "B \left[\begin{array}{ccc}3&4\\1&0\\\end{array}\right] \cdot A \left[\begin{array}{ccc}2&1\\3&1\\\end{array}\right] \\ \\ \\ B\cdot A= \left[\begin{array}{ccc}((3\cdot2)+(4\cdot3))~~~~&((3\cdot1)+(4\cdot1))\\((1\cdot2)+(0\cdot3))~~~~&((1\cdot1)+(0\cdot1))\\\end{array}\right] \\ \\ \\ B\cdot A= \left[\begin{array}{ccc}(6+12)~~~~&(3+4)\\(2+0)~~~~&(1+0)\\\end{array}\right] \\ \\ \\ \boxed{\boxed{B\cdot A= \left[\begin{array}{ccc}18&7\\2&1\\\end{array}\right]}}")
C)
Podemos obter a matriz A², multiplicando A por A. então A²=A*A;
![A^2=A \left[\begin{array}{ccc}2&1\\3&1\\\end{array}\right]\cdot A\left[\begin{array}{ccc}2&1\\3&1\\\end{array}\right] \\ \\ \\ A^2= \left[\begin{array}{ccc}((2\cdot2)+(1\cdot3))~~~~&((2\cdot1)+(1\cdot1))\\((3\cdot2)+(1\cdot3))~~~~&((3\cdot1)+(1\cdot1))\\\end{array}\right] \\ \\ \\ A^2= \left[\begin{array}{ccc}(4+3)~~~~&(2+1)\\(6+3)~~~~&(3+1)\\\end{array}\right] \\ \\ \\ \boxed{\boxed{A^2= \left[\begin{array}{ccc}7&3\\9&4\\\end{array}\right]}}](https://tex.z-dn.net/?f=A%5E2%3DA+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26amp%3B1%5C%5C3%26amp%3B1%5C%5C%5Cend%7Barray%7D%5Cright%5D%5Ccdot+A%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26amp%3B1%5C%5C3%26amp%3B1%5C%5C%5Cend%7Barray%7D%5Cright%5D++%5C%5C+%5C%5C+%5C%5C+A%5E2%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%28%282%5Ccdot2%29%2B%281%5Ccdot3%29%29%7E%7E%7E%7E%26amp%3B%28%282%5Ccdot1%29%2B%281%5Ccdot1%29%29%5C%5C%28%283%5Ccdot2%29%2B%281%5Ccdot3%29%29%7E%7E%7E%7E%26amp%3B%28%283%5Ccdot1%29%2B%281%5Ccdot1%29%29%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%5C%5C+%5C%5C+A%5E2%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%284%2B3%29%7E%7E%7E%7E%26amp%3B%282%2B1%29%5C%5C%286%2B3%29%7E%7E%7E%7E%26amp%3B%283%2B1%29%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%5C%5C+%5C%5C+%5Cboxed%7B%5Cboxed%7BA%5E2%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D7%26amp%3B3%5C%5C9%26amp%3B4%5C%5C%5Cend%7Barray%7D%5Cright%5D%7D%7D%0A "A^2=A \left[\begin{array}{ccc}2&1\\3&1\\\end{array}\right]\cdot A\left[\begin{array}{ccc}2&1\\3&1\\\end{array}\right] \\ \\ \\ A^2= \left[\begin{array}{ccc}((2\cdot2)+(1\cdot3))~~~~&((2\cdot1)+(1\cdot1))\\((3\cdot2)+(1\cdot3))~~~~&((3\cdot1)+(1\cdot1))\\\end{array}\right] \\ \\ \\ A^2= \left[\begin{array}{ccc}(4+3)~~~~&(2+1)\\(6+3)~~~~&(3+1)\\\end{array}\right] \\ \\ \\ \boxed{\boxed{A^2= \left[\begin{array}{ccc}7&3\\9&4\\\end{array}\right]}}")
Caso não consiga visualizar, tente abrir pelo navegador:
http://brainly.com.br/tarefa/7776711
A multiplicação de matrizes é feito através de linhas por colunas
A)
B)
C)
Podemos obter a matriz A², multiplicando A por A. então A²=A*A;
Caso não consiga visualizar, tente abrir pelo navegador:
http://brainly.com.br/tarefa/7776711
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