MATRIZ AJUDEM
Se a ![\left[\begin{array}{c}1&-2&-3\end{array}\right]](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%26amp%3B-2%26amp%3B-3%5Cend%7Barray%7D%5Cright%5D "\left[\begin{array}{c}1&-2&-3\end{array}\right]")
+ b ![\left[\begin{array}{c}2&3&-1\\\end{array}\right]](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%26amp%3B3%26amp%3B-1%5C%5C%5Cend%7Barray%7D%5Cright%5D+ "\left[\begin{array}{c}2&3&-1\\\end{array}\right]")
+ c ![\left[\begin{array}{c}3&2&1\\\end{array}\right]](https://tex.z-dn.net/?f=+++%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D3%26amp%3B2%26amp%3B1%5C%5C%5Cend%7Barray%7D%5Cright%5D+ "\left[\begin{array}{c}3&2&1\\\end{array}\right]")
= ![\left[\begin{array}{c}0&0&0\\\end{array}\right]](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%26amp%3B0%26amp%3B0%5C%5C%5Cend%7Barray%7D%5Cright%5D+ "\left[\begin{array}{c}0&0&0\\\end{array}\right]")
determine os valores de a,b e c.
Soluções para a tarefa
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Basta lembrar que quando multiplicamos um numero escalar por uma matriz, basta multiplicar cada ele elemento dessa matriz por esse numero:
![a \left[\begin{array}{c}1&-2&-3\end{array}\right] + b \left[\begin{array}{c}2&3&-1\\\end{array}\right] +c \left[\begin{array}{c}3&2&1\\\end{array}\right] = \left[\begin{array}{c}0&0&0\\\end{array}\right] \\ \\ \left[\begin{array}{c}a&-2a&-3a\end{array}\right] + \left[\begin{array}{c}2b&3b&-b\\\end{array}\right] + \left[\begin{array}{c}3c&2c&c\\\end{array}\right] = \left[\begin{array}{c}0&0&0\\\end{array}\right] \\ \\ \left \{ {{a + 2b + 3c=0} \atop {-2a+3b+2c=0}} \atop {-3a-b+c=0}} \right.](https://tex.z-dn.net/?f=a+%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D1%26amp%3B-2%26amp%3B-3%5Cend%7Barray%7D%5Cright%5D+%2B+b+%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2%26amp%3B3%26amp%3B-1%5C%5C%5Cend%7Barray%7D%5Cright%5D+%2Bc+%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D3%26amp%3B2%26amp%3B1%5C%5C%5Cend%7Barray%7D%5Cright%5D+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%26amp%3B0%26amp%3B0%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%5C%5C+%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Da%26amp%3B-2a%26amp%3B-3a%5Cend%7Barray%7D%5Cright%5D+%2B+%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D2b%26amp%3B3b%26amp%3B-b%5C%5C%5Cend%7Barray%7D%5Cright%5D+%2B+%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D3c%26amp%3B2c%26amp%3Bc%5C%5C%5Cend%7Barray%7D%5Cright%5D+%3D+%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%26amp%3B0%26amp%3B0%5C%5C%5Cend%7Barray%7D%5Cright%5D+%5C%5C+%5C%5C+%5Cleft+%5C%7B+%7B%7Ba+%2B+2b+%2B+3c%3D0%7D+%5Catop+%7B-2a%2B3b%2B2c%3D0%7D%7D+%5Catop+%7B-3a-b%2Bc%3D0%7D%7D+%5Cright. "a \left[\begin{array}{c}1&-2&-3\end{array}\right] + b \left[\begin{array}{c}2&3&-1\\\end{array}\right] +c \left[\begin{array}{c}3&2&1\\\end{array}\right] = \left[\begin{array}{c}0&0&0\\\end{array}\right] \\ \\ \left[\begin{array}{c}a&-2a&-3a\end{array}\right] + \left[\begin{array}{c}2b&3b&-b\\\end{array}\right] + \left[\begin{array}{c}3c&2c&c\\\end{array}\right] = \left[\begin{array}{c}0&0&0\\\end{array}\right] \\ \\ \left \{ {{a + 2b + 3c=0} \atop {-2a+3b+2c=0}} \atop {-3a-b+c=0}} \right.")
A resolução do sistema se encontra abaixo
A resolução do sistema se encontra abaixo
Anexos:
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