Question

A matriz quadrada de ordem 2,M=(mij)com mij=3i-2j, é
a)(4 1 )
(2 -1)
b)(0 -2)
(4 1)
c)(-1 4)
(4 2)
d)(1 -1)
(4 2)
e)(0 2)
(-1 1)

Answer 1

✅ Após resolver os cálculos, concluímos que a matriz procurada é:

                $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf M = \begin{bmatrix}1 & -1\\4 & 2 \end{bmatrix}\:\:\:}}\end{gathered} }$

Portanto, a opção correta é:

                     $\Large\displaystyle\text{ \begin{gathered}\boxed{\boxed{\:\:\:\bf Letra\:D\:\:\:}}\end{gathered} }$

Seja a matriz:

        $\Large\displaystyle\begin{gathered} M_{2\times2},\:\:\:\textrm{tal\:que}\:\:m_{(ij)} = 3i - 2j\end{gathered}$

Então, temos:

        $\Large\displaystyle\begin{gathered}M = \begin{bmatrix}3\cdot1 - 2\cdot1 & 3\cdot1 - 2\cdot2\\ 3\cdot2 - 2\cdot1 & 3\cdot2 - 2\cdot2\end{bmatrix}\end{gathered}$

               $\Large\displaystyle\begin{gathered}=\begin{bmatrix} 3 - 2 & 3 - 4\\6 - 2 & 6 - 4\end{bmatrix}\end{gathered}$

               $\Large\displaystyle\begin{gathered}= \begin{bmatrix} 1 & -1\\4 & 2\end{bmatrix}\end{gathered}$

✅ Portanto, a matriz procurada é:

         $\Large\displaystyle\begin{gathered}M = \begin{bmatrix} 1 & -1\\4 & 2\end{bmatrix}\end{gathered}$

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