Question

determine a matriz D resultante da operação A + B – C.

$A=\left[\begin{array}{ccc}1&2&3\\-4&5&6\\4&6&8\end{array}\right] B=\left[\begin{array}{ccc}-7&-8&9\\12&6&5\\8&7&4\end{array}\right] C=\left[\begin{array}{ccc}2&3&-4\\6&7&1\\2&8&7\end{array}\right]$

Answer 1

Conteúdo:

         Operações com matrizes

Resolução:

• Para resolvemos temos que entender sobre adição e subtração de matrizes, um exemplo básico seria:

Adição:

$\large {\text { \sf A \quad \quad + \quad\quad B \atop {\sf \left[\begin{array}{ccc}\sf 21&\sf 17&\sf 15\\ \sf 18& \sf 13& \sf 9\\ \sf 11& \sf 9& \sf3\end{array}\right] \quad \left[\begin{array}{ccc} \sf 23 & \sf 14 & \sf 17\\ \sf 17& \sf 16& \sf 8\\ \sf 18 & \sf 10 & \sf 5\end{array}\right] } }}$

$\large { \sf = \left[\begin{array}{ccc} \sf 21+23& \sf 17+14& \sf 15+17\\ \sf 18+17& \sf 13+16& \sf 9+8\\ \sf 11+18& \sf 9+10& \sf 3+5 \end{array}\right] = \left[\begin{array}{ccc}\sf44&\sf31&\sf32\\ \sf35&\sf29&\sf17\\ \sf 29& \sf 19& \sf 8\end{array}\right] }$

Subtração:

$\large {\text { \sf A \quad \quad - \quad\quad B \atop {\sf \left[\begin{array}{ccc}\sf 21&\sf 17&\sf 15\\ \sf 18& \sf 13& \sf 9\\ \sf 11& \sf 9& \sf3\end{array}\right] \quad \left[\begin{array}{ccc} \sf 23 & \sf 14 & \sf 17\\ \sf 17& \sf 16& \sf 8\\ \sf 18 & \sf 10 & \sf 5\end{array}\right] } }}$

$\large { \sf = \left[\begin{array}{ccc} \sf 21-23& \sf 17-14& \sf 15-17\\ \sf 18-17& \sf 13-16& \sf 9-8\\ \sf 11-18& \sf 9-10& \sf 3-5 \end{array}\right] = \left[\begin{array}{ccc}\sf-2&\sf3&\sf-2\\ \sf1&\sf-3&\sf1\\ \sf -7& \sf -1& \sf -2\end{array}\right] }$

• Tendo esses dois exemplos conseguimos resolver:

Resolveremos primeiro a adição (A+B)....

$\large { \sf \sf \left[\begin{array}{ccc}\sf 1&\sf 2&\sf 3\\ \sf -4& \sf 5& \sf 6\\ \sf 4& \sf 6& \sf8\end{array}\right] + \left[\begin{array}{ccc} \sf -7 & \sf -8 & \sf 9\\ \sf 12& \sf 6& \sf 5\\ \sf 8 & \sf 7 & \sf 4\end{array}\right] = \left[\begin{array}{ccc}\sf -6& \sf -6 & \sf 12\\ \sf 8& \sf 11& \sf 11 \\ \sf 12 & \sf 13& \sf 12\end{array}\right] }$

• Agora resolver a subtração:

$\large { \sf \left[\begin{array}{ccc}\sf -6& \sf -6 & \sf 12\\ \sf 8& \sf 11& \sf 11 \\ \sf 12 & \sf 13& \sf 12\end{array}\right] - \left[\begin{array}{ccc}\sf 2& \sf 3 & \sf -4\\ \sf 6& \sf 7& \sf 1 \\ \sf 2 & \sf 8& \sf 7\end{array}\right] = \left[\begin{array}{ccc}\sf -8& \sf -9 & \sf 8\\ \sf 2& \sf 4& \sf 10 \\ \sf 10 & \sf 5& \sf 5\end{array}\right] }$

• Portanto:

$\large {\boxed {\boxed {\sf D = \left[\begin{array}{ccc}\sf -8& \sf -9 & \sf 8\\ \sf 2& \sf 4& \sf 10 \\ \sf 10 & \sf 5& \sf 5\end{array}\right] }}}$     $\checkmark$

Answer 2

Sua questão pede para encontrarmos a matriz D sendo a mesma igual a A + B – C . Para encontramos a matriz D é só fazermos A + B – C, a questão nos da os respectivos valores de A , B e C são eles:

$\large\begin{array}{lr}\sf \red{A}=\left[\begin{array}{ccc}1&2&3\\-4&5&6\\4&6&8\end{array}\right]\end{array}$

$\large\begin{array}{lr}\sf \red{B}=\left[\begin{array}{ccc}-7&-8&9\\12&6&5\\8&7&4\end{array}\right]\end{array}$

$\large\begin{array}{lr}\sf \red{C}=\left[\begin{array}{ccc}2&3&-4\\6&7&1\\2&8&7\end{array}\right]\end{array}$

Portanto  A + B – C é igual à:

$\large\begin{array}{lr}\sf\left[\begin{array}{ccc}1&2&3\\-4&5&6\\4&6&8\end{array}\right] +\left[\begin{array}{ccc}-7&-8&9\\12&6&5\\8&7&4\end{array}\right] - \left[\begin{array}{ccc}2&3&-4\\6&7&1\\2&8&7\end{array}\right]\end{array}$

$\large\begin{array}{lr}\sf\left[\begin{array}{ccc}1+(-7)&2+(-8)&3+9\\-4+12&5+6&6+5\\4+8&6+7&8+4\end{array}\right] - \left[\begin{array}{ccc}2&3&-4\\6&7&1\\2&8&7\end{array}\right]\end{array}$

$\large\begin{array}{lr}\sf\left[\begin{array}{ccc}-6&-6&12\\8&11&11\\12&13&12\end{array}\right] - \left[\begin{array}{ccc}2&3&-4\\6&7&1\\2&8&7\end{array}\right]\end{array}$

$\large\begin{array}{lr}\sf\left[\begin{array}{ccc}-6-2&-6-3&12-4\\8-6&11-7&11-1\\12-2&13-8&12-7\end{array}\right]\end{array}$

$\large\begin{array}{lr}\sf \sf\left[\begin{array}{ccc}-8&-9&8\\2&4&10\\10&5&5\end{array}\right]\end{array}$

$\boxed{\boxed{\large\begin{array}{lr}\sf \red{D} =\sf\left[\begin{array}{ccc}-8&-9&8\\2&4&10\\10&5&5\end{array}\right]\end{array}}}$

Caso queria aprender sobre operações com matrizes clique nos links abaixo.

$\rightarrow$ ( brainly.com.br/tarefa/44898724 )

$\rightarrow$ ( brainly.com.br/tarefa/44413511 )

$\rightarrow$ ( brainly.com.br/tarefa/44333214 )

$\rightarrow$ ( brainly.com.br/tarefa/44184303 )

Espero ter ajudado.

Bons estudos.

• Att. FireClassis.