Question

O produto AB entre as matrizes A=(2,1)(-1,3) e B= (2,0) (1,4):

Answer 1

✅ Após resolver o produto das referidas matrizes, concluímos que o resultado é:

                          $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf \begin{pmatrix} 5 & 4\\1 & 12\end{pmatrix}\:\:\:}}\end{gathered} }$  

Sejam as matrizes:

                          $\Large\displaystyle\begin{gathered} A = \begin{pmatrix}2 & 1\\ -1 & 3\end{pmatrix}\end{gathered}$

                           $\Large\displaystyle\begin{gathered} B = \begin{pmatrix}2 & 0\\1 & 4 \end{pmatrix}\end{gathered}$

Calculando o produto AB das matrizes, nesta ordem, temos:

 $\Large\displaystyle\begin{gathered} \begin{pmatrix} 2 & 1\\-1 & 3\end{pmatrix}\cdot \begin{pmatrix} 2 & 0\\1 & 4\end{pmatrix} = \begin{pmatrix} 2\cdot2 + 1\cdot1 & 2\cdot0 + 1\cdot4\\(-1)\cdot2 + 3\cdot1 & (-1)\cdot0 + 3\cdot4\end{pmatrix}\end{gathered}$

                                          $\Large\displaystyle\begin{gathered} = \begin{pmatrix}4 + 1 & 0 + 4\\-2 + 3 & 0 + 12 \end{pmatrix}\end{gathered}$

                                          $\Large\displaystyle\begin{gathered} = \begin{pmatrix} 5 & 4\\1 & 12 \end{pmatrix}\end{gathered}$

✅ Portanto, a matriz resultante é:

                       $\Large\displaystyle\begin{gathered} \begin{pmatrix} 5 & 4\\1 & 12\end{pmatrix}\end{gathered}$

$\LARGE\displaystyle\text{ \begin{gathered} \underline{\boxed{\boldsymbol{\:\:\:Bons \:estudos!!\:\:\:Boa\: sorte!!\:\:\:}}}\end{gathered} }$

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