Question

Questão 4 - Dada as matrizes:

D+É é a matriz:

A)| 2 1 0 |
| 0 1 0 |
| 1 2 1 |

B) | 0 1 1 |
| 3 4 2 |

C) | 0 1 1 |
| 3 4 2 |
| 3 4 2 |

D) | 5 1 0 |
| 1 3 0 |
| 3 5 2 |

E) | 7 6 5 |
| -2 1 3 |
| 7 3 7 |



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Answer 1

Para que possamos somar ou subtrair matrizes devemos somar - subtrair números de posições iguais, veja abaixo um exemplo.

$\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] + \left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right]$

Agora devemos somar os termos de posições iguais. Veja:

$\left[\begin{array}{ccc}\boxed{\sf 1}&2&3\\4&5&6\\7&8&9\end{array}\right] +\left[\begin{array}{ccc}\boxed{\sf 1}&2&3\\4&5&6\\7&8&9\end{array}\right] \rightarrow \left[\begin{array}{ccc}\underline{\boxed{\sf 1+1}}&&\\&&\\&&\end{array}\right]$

$\left[\begin{array}{ccc}1&\boxed{\sf 2}&3\\4&5&6\\7&8&9\end{array}\right] +\left[\begin{array}{ccc} 1&\boxed{\sf 2}&3\\4&5&6\\7&8&9\end{array}\right] \rightarrow \left[\begin{array}{ccc}&\underline{\boxed{\sf 2+2}}&\\&&\\&&\end{array}\right]$

$\left[\begin{array}{ccc}1&2&\boxed{\sf 3}\\4&5&6\\7&8&9\end{array}\right] +\left[\begin{array}{ccc} 1&2&\boxed{\sf 3}\\4&5&6\\7&8&9\end{array}\right] \rightarrow \left[\begin{array}{ccc}&&\underline{\boxed{\sf 3+3}}\\&&\\&&\end{array}\right]$

$\left[\begin{array}{ccc}1&2&3\\\boxed{\sf 4}&5&6\\7&8&9\end{array}\right] +\left[\begin{array}{ccc} 1&2&3\\\boxed{\sf 4}&5&6\\7&8&9\end{array}\right] \rightarrow \left[\begin{array}{ccc}&&\\\underline{\boxed{\sf 4+4 }}&&\\&&\end{array}\right]$

$\left[\begin{array}{ccc}1&2&3\\4&\boxed{\sf 5}&6\\7&8&9\end{array}\right] +\left[\begin{array}{ccc} 1&2&3\\4&\boxed{\sf 5}&6\\7&8&9\end{array}\right] \rightarrow \left[\begin{array}{ccc}&&\\&\underline{\boxed{\sf 5+5}}&\\&&\end{array}\right]$

$\left[\begin{array}{ccc}1&2&3\\4&5&\boxed{\sf 6}\\7&8&9\end{array}\right] +\left[\begin{array}{ccc} 1&2&3\\4& 5&\boxed{\sf 6}\\7&8&9\end{array}\right] \rightarrow \left[\begin{array}{ccc}&&\\&&\underline{\boxed{\sf 6+6}}\\&&\end{array}\right]$

$\left[\begin{array}{ccc}1&2&3\\4&5&6\\\boxed{\sf 7}&8&9\end{array}\right] +\left[\begin{array}{ccc} 1&2&3\\4& 5&6\\\boxed{\sf 7}&8&9\end{array}\right] \rightarrow \left[\begin{array}{ccc}&&\\&&\\\underline{\boxed{\sf 7+7}}&&\end{array}\right]$

$\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&\boxed{\sf 8}&9\end{array}\right] +\left[\begin{array}{ccc} 1&2&3\\4& 5&6\\7&\boxed{\sf 8}&9\end{array}\right] \rightarrow \left[\begin{array}{ccc}&&\\&&\\&\underline{\boxed{\sf 8+8}}&\end{array}\right]$

$\left[\begin{array}{ccc}1&2&3\\4&5&6\\7& 8&\boxed{\sf 9}\end{array}\right] +\left[\begin{array}{ccc} 1&2&3\\4& 5&6\\7&8&\boxed{\sf 9}\end{array}\right] \rightarrow \left[\begin{array}{ccc}&&\\&&\\&&\underline{\boxed{\sf 9+9}}\end{array}\right]$

Portanto:

$\left[\begin{array}{ccc}1&2&3\\4&5&6\\7& 8& 9\end{array}\right] +\left[\begin{array}{ccc} 1&2&3\\4& 5&6\\7&8&9\end{array}\right] \rightarrow \left[\begin{array}{ccc}1+1&2+2&3+3\\4+4&5+5&6+6\\7+7&8+8&9+9\end{array}\right]$

$\left[\begin{array}{ccc}2&4&6\\8&10&12\\14&16&18\end{array}\right]$

Importante!

Isso foi apenas um exemplo ... a resolução da sua questão está abaixo.

( Sua questão: )

Dada as matrizes:

$\sf D=\left[\begin{array}{ccc}1&5&2\\-1&0&1\\3&2&4\end{array}\right]$

$\sf E=\left[\begin{array}{ccc}6&1&3\\-1&1&2\\4&1&3\end{array}\right]$

D + E é a matriz:

$\sf \left[\begin{array}{ccc}7&6&5\\-2&1&3\\7&3&7\end{array}\right] \leftarrow \sf Resposta\ ( E).$

( Resolução: )

$\sf \left[\begin{array}{ccc}1&5&2\\-1&0&1\\3&2&4\end{array}\right]+ \sf \left[\begin{array}{ccc}6&1&3\\-1&1&2\\4&1&3\end{array}\right] =>$

$\sf \left[\begin{array}{ccc}1+6&5+1&2+3\\-1+(-1)&0+1&1+2\\3+4&2+1&4+3\end{array}\right] =>$

$=>\sf \left[\begin{array}{ccc}7&6&5\\-2&1&3\\7&3&7\end{array}\right]$

Concluirmos então que a alternativa correta é a E.

Espero ter ajudado.

Bons estudos.

• Att. FireClassis.