Question

Dadas as matrizes me ajude

Answer 1

Resposta:

Atransposta * Btransposta = Res

Res =  1   -1   -4

         8    10   16

         6     3     0

Answer 2

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$\sf\large\green{\boxed{\blue{ \ \ \ (B^t \cdot A^t)_{2,2}=\left[\begin{array}{cc}1&8\\\\11&10\\\end{array}\right] \ \ \ }}}$

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$\bf\large\green{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad}}$

$\green{\rm\underline{EXPLICAC_{\!\!\!,}\tilde{A}O\ PASSO{-}A{-}PASSO\ \ \ }}$✍

❄☃ $\sf(\gray{+}\ \red{cores}\ \blue{com}\ \pink{o}\ \orange{App}\ \green{Brainly})$ ☘☀

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☺lá, Hoody, como tens passado nestes tempos de quarentena⁉ E os estudos à distância, como vão⁉ Espero que bem❗

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☔ Temos que a matriz transposta de A_{i,j}, denotada A_{i,j}^{t}, é dada pela inversão de i e j, ou seja, pelatransposição de todas as suas linhas para colunas (o que é equivalente a dizer que ela é dada pela transposição de todas as colunas por linhas).

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$\rm\large\red{\boxed{\pink{\boxed{\begin{array}{rcl} & & \\ & \orange{ a^{t}_{ij}  = a_{ji} } & \\ & & \\ \end{array}}}}}$

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☔ Nossa matriz é da forma  

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

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☔ Portanto nossa nova matriz será da forma

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$A^{t}_{3,2}=\left[\begin{array}{cc}1&-1\\\\2&4\\\\3&0\\\end{array}\right]$

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☔ De forma semelhante, para a matriz B, temos que

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$B_{3,2}=\left[\begin{array}{cc}2&1\\\\1&2\\\\0&4\\\end{array}\right]$

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☔ Portanto nossa nova matriz será da forma

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$(B^t \cdot A^t)_{3,2}=\left[\begin{array}{cc}c_{11}&c_{12}\\\\c_{21}&c_{22}\\\\c_{31}&c_{32}\\\end{array}\right]$

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$(B^t \cdot A^t)_{3,2}=\left[\begin{array}{cc}a_{11} \cdot b_{11} + a_{12} \cdot b_{21} + a_{13} \cdot b_{31}&a_{11} \cdot b_{12} + a_{12} \cdot b_{22} + a_{13} \cdot b_{32}\\\\a_{21} \cdot b_{11} + a_{22} \cdot b_{21} + a_{23} \cdot b_{31}&a_{21} \cdot b_{12} + a_{22} \cdot b_{22} + a_{23} \cdot b_{32}\\\\a_{31} \cdot b_{11} + a_{32} \cdot b_{21} + a_{33} \cdot b_{31}&a_{31} \cdot b_{12} + a_{32} \cdot b_{22} + a_{33} \cdot b_{32}\\\end{array}\right]$

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$(B^t \cdot A^t)_{2,2}=\left[\begin{array}{cc}2 \cdot 1 + 1 \cdot (-1) + 0 \cdot 3&2 \cdot 2 + 1 \cdot 4 + 0 \cdot 0\\\\1 \cdot 1 + 2 \cdot (-1) + 4 \cdot 3&1 \cdot 2 + 2 \cdot 4 + 4 \cdot 0\\\end{array}\right]$

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$\sf\large\green{\boxed{\blue{ \ \ \ (B^t \cdot A^t)_{2,2}=\left[\begin{array}{cc}1&8\\\\11&10\\\end{array}\right]\ \ \ }}}$ ✅

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$\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad}}$☁

☕ $\bf\large\blue{Bons\ estudos.}$

($\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios}$) ☄

$\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }}\LaTeX$✍

❄☃ $\sf(\gray{+}\ \red{cores}\ \blue{com}\ \pink{o}\ \orange{App}\ \green{Brainly})$ ☘☀

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$\large\textit{"Absque\ sudore\ et\ labore}$

$\large\textit{nullum\ opus\ perfectum\ est."}$