a) Sejam as matrizes A = 1 2 3 e B= - 1 0 2 obtenha a matriz X no seguinte caso X + A = 2b
4 5 6 5 6 8
7 8 9 4 -3 6
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Aplicando as propriedades de matrizes
![A= \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \\ \\ \\ B= \left[\begin{array}{ccc}-1&0&2\\5&6&8\\4&-3&6\end{array}\right]](https://tex.z-dn.net/?f=A%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B2%26amp%3B3%5C%5C4%26amp%3B5%26amp%3B6%5C%5C7%26amp%3B8%26amp%3B9%5Cend%7Barray%7D%5Cright%5D++%5C%5C++%5C%5C++%5C%5C+B%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26amp%3B0%26amp%3B2%5C%5C5%26amp%3B6%26amp%3B8%5C%5C4%26amp%3B-3%26amp%3B6%5Cend%7Barray%7D%5Cright%5D+ "A= \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \\ \\ \\ B= \left[\begin{array}{ccc}-1&0&2\\5&6&8\\4&-3&6\end{array}\right]")
Para encontrar a matriz "2b", basta multiplicar cada elemento da matriz por 2.
![2B= \left[\begin{array}{ccc}-1\cdot(2)&0\cdot(2)&2\cdot(2)\\5\cdot(2)&6\cdot(2)&8\cdot(2)\\4\cdot(2)&-3\cdot(2)&6\cdot(2)\end{array}\right] \\ \\ \\ \\ \boxed{2B= \left[\begin{array}{ccc}-2&0&4\\10&12&16\\8&-6&12\end{array}\right]}](https://tex.z-dn.net/?f=2B%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%5Ccdot%282%29%26amp%3B0%5Ccdot%282%29%26amp%3B2%5Ccdot%282%29%5C%5C5%5Ccdot%282%29%26amp%3B6%5Ccdot%282%29%26amp%3B8%5Ccdot%282%29%5C%5C4%5Ccdot%282%29%26amp%3B-3%5Ccdot%282%29%26amp%3B6%5Ccdot%282%29%5Cend%7Barray%7D%5Cright%5D+%5C%5C++%5C%5C++%5C%5C++%5C%5C+%5Cboxed%7B2B%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%26amp%3B0%26amp%3B4%5C%5C10%26amp%3B12%26amp%3B16%5C%5C8%26amp%3B-6%26amp%3B12%5Cend%7Barray%7D%5Cright%5D%7D "2B= \left[\begin{array}{ccc}-1\cdot(2)&0\cdot(2)&2\cdot(2)\\5\cdot(2)&6\cdot(2)&8\cdot(2)\\4\cdot(2)&-3\cdot(2)&6\cdot(2)\end{array}\right] \\ \\ \\ \\ \boxed{2B= \left[\begin{array}{ccc}-2&0&4\\10&12&16\\8&-6&12\end{array}\right]}")
Agora que já temos a matriz "2b", basta subtrair (2b - A)
![X=2B-A \\ \\ X= \left[\begin{array}{ccc}-2&0&4\\10&12&16\\8&-6&12\end{array}\right]}~~~~~~-~~~~~~\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \\ \\ \\ X= \left[\begin{array}{ccc}(-2-1)&(0-2)&(4-3)\\(10-4)&(12-5)&(16-6)\\(8-7)&(-6-8)&(12-9)\end{array}\right] \\ \\ \\ \\ \boxed{\boxed{X= \left[\begin{array}{ccc}-3&-2&1\\6&7&10\\1&-14&3\end{array}\right] }}](https://tex.z-dn.net/?f=X%3D2B-A+%5C%5C++%5C%5C++X%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-2%26amp%3B0%26amp%3B4%5C%5C10%26amp%3B12%26amp%3B16%5C%5C8%26amp%3B-6%26amp%3B12%5Cend%7Barray%7D%5Cright%5D%7D%7E%7E%7E%7E%7E%7E-%7E%7E%7E%7E%7E%7E%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26amp%3B2%26amp%3B3%5C%5C4%26amp%3B5%26amp%3B6%5C%5C7%26amp%3B8%26amp%3B9%5Cend%7Barray%7D%5Cright%5D+%5C%5C++%5C%5C++%5C%5C+X%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%28-2-1%29%26amp%3B%280-2%29%26amp%3B%284-3%29%5C%5C%2810-4%29%26amp%3B%2812-5%29%26amp%3B%2816-6%29%5C%5C%288-7%29%26amp%3B%28-6-8%29%26amp%3B%2812-9%29%5Cend%7Barray%7D%5Cright%5D++%5C%5C++%5C%5C++%5C%5C++%5C%5C+%5Cboxed%7B%5Cboxed%7BX%3D++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-3%26amp%3B-2%26amp%3B1%5C%5C6%26amp%3B7%26amp%3B10%5C%5C1%26amp%3B-14%26amp%3B3%5Cend%7Barray%7D%5Cright%5D+%7D%7D "X=2B-A \\ \\ X= \left[\begin{array}{ccc}-2&0&4\\10&12&16\\8&-6&12\end{array}\right]}~~~~~~-~~~~~~\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \\ \\ \\ X= \left[\begin{array}{ccc}(-2-1)&(0-2)&(4-3)\\(10-4)&(12-5)&(16-6)\\(8-7)&(-6-8)&(12-9)\end{array}\right] \\ \\ \\ \\ \boxed{\boxed{X= \left[\begin{array}{ccc}-3&-2&1\\6&7&10\\1&-14&3\end{array}\right] }}")
Caso não consiga visualizar as imagens, tente abrir pelo navegador.
https://brainly.com.br/tarefa/8340023
Aplicando as propriedades de matrizes
Para encontrar a matriz "2b", basta multiplicar cada elemento da matriz por 2.
Agora que já temos a matriz "2b", basta subtrair (2b - A)
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