Question

resolva a matriz, por favor me ajude nessa questão.
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Answer 1

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⠀⠀☞ A matriz do item a) será quadrada de ordem dois e de valores a₁₁ = 1; a₁₂ = 8; a₂₁ = (-1); a₂₂ = 6. A matriz do item b) será também quadrada de ordem dois e de valores a₁₁ = 12; a₁₂ = 17; a₂₁ = 12; a₂₂ = 5. ✅

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⚡ " -O que é uma matriz transposta?"

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➡️⠀É a transformação de uma matriz A em outra matriz B em que as linhas da matriz A serão as colunas da matriz B e as colunas da matriz A serão as linhas da matriz B, ou seja:

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$\Large\red{\boxed{\pink{\boxed{\begin{array}{rcl}&&\\&\orange{\sf A_{ij} = A_{ji}^t}&\\&&\\\end{array}}}}}$

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$\text{\pink{ \Longrightarrow }~\Large\orange{ \sf i }}$ sendo o índice do número de linhas da matriz A e de colunas da matriz B;

$\text{\pink{ \Longrightarrow }~\Large\orange{ \sf j }}$ sendo o índice do número de colunas da matriz A e de linhas da matriz B;

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➡️⠀Com isto temos que:

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$\LARGE\blue{\sf a) A^t + B - C}$

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

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⚡ " -Como somar e subtrair matrizes?"

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➡️⠀Após verificar que as matrizes possuem a mesma quantidade de linhas e de colunas, devemos somar e subtrair os valores de mesma posição nas matrizes:

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

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$\Large\blue{= \left[\begin{array}{cc}\sf 1&\sf 8\\&\\\sf (-1)&\sf 6\end{array}\right]}$  

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$\huge\green{\boxed{\rm~~~\red{a)}~\blue{ \left[\begin{array}{cc}\sf 1&\sf 8\\&\\\sf (-1)&\sf 6\end{array}\right] }~~~}}$ ✅

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➡️⠀Já para o item b) temos que:

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$\LARGE\blue{\sf b) (5 \cdot A + B)^t + \dfrac{C}{2}}$

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➡️⠀Inicialmente vamos encontrar o resultado do interior dos parênteses:

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$\Large\blue{\sf 5 \cdot A + B = 5 \cdot \left[\begin{array}{cc}\sf 2&\sf 1\\&\\\sf 3&\sf 2\end{array}\right] + \left[\begin{array}{cc}\sf 1&\sf 5\\&\\\sf 2&\sf -2\end{array}\right]}$

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$\Large\blue{ = \left[\begin{array}{cc}\sf 5 \cdot 2&\sf 5 \cdot 1\\&\\\sf 5 \cdot 3&\sf 5 \cdot 2\end{array}\right] + \left[\begin{array}{cc}\sf 1&\sf 5\\&\\\sf 2&\sf -2\end{array}\right]}$

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$\Large\blue{ = \left[\begin{array}{cc}\sf 10&\sf 5\\&\\\sf 15&\sf 10\end{array}\right] + \left[\begin{array}{cc}\sf 1&\sf 5\\&\\\sf 2&\sf -2\end{array}\right]}$

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$\Large\blue{ = \left[\begin{array}{cc}\sf 10 + 1&\sf 5 + 5\\&\\\sf 15 + 2&\sf 10 + (-2)\end{array}\right]}$

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$\Large\blue{ = \left[\begin{array}{cc}\sf 11&\sf 10\\&\\\sf 17&\sf 8\end{array}\right]}$

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➡️⠀Podemos agora encontrar a matriz transposta de 5A + B e somar com o produto de C por 1/2:

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$\Large\blue{\sf (5 \cdot A + B)^t + \dfrac{C}{2} = \left[\begin{array}{cc}\sf 11&\sf 17\\&\\\sf 10&\sf 8\end{array}\right] + \dfrac{1}{2} \cdot \left[\begin{array}{cc}\sf 2&\sf 0\\&\\\sf 4&\sf -6\end{array}\right]}$

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$\Large\blue{ = \left[\begin{array}{cc}\sf 11&\sf 17\\&\\\sf 10&\sf 8\end{array}\right] + \left[\begin{array}{cc}\sf \dfrac{1}{2} \cdot 2&\sf \dfrac{1}{2} \cdot 0\\&\\\sf \dfrac{1}{2} \cdot 4&\sf \dfrac{1}{2} \cdot (-6)\end{array}\right]}$

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$\Large\blue{ = \left[\begin{array}{cc}\sf 11&\sf 17\\&\\\sf 10&\sf 8\end{array}\right] + \left[\begin{array}{cc}\sf 1&\sf 0\\&\\\sf 2&\sf (-3)\end{array}\right]}$

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$\Large\blue{ = \left[\begin{array}{cc}\sf 11 + 1&\sf 17 + 0\\&\\\sf 10 + 2&\sf 8 + (-3)\end{array}\right]}$

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$\Large\blue{ = \left[\begin{array}{cc}\sf 12&\sf 17\\&\\\sf 12&\sf 5\end{array}\right]}$

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$\huge\green{\boxed{\rm~~~\red{a)}~\blue{ \left[\begin{array}{cc}\sf 12&\sf 17\\&\\\sf 12&\sf 5\end{array}\right]}~~~}}$ ✅

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

⠀⠀☀️ Leia mais sobre matrizes:

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✈ https://brainly.com.br/tarefa/39722589

✈ https://brainly.com.br/tarefa/37460651

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

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

⠀⠀⠀⠀☕ $\Large\blue{\text{\bf Bons~estudos.}}$

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

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

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

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$\Huge\green{\text{ \underline{\red{\mathbb{S}}\blue{\mathfrak{oli}}~}~\underline{\red{\mathbb{D}}\blue{\mathfrak{eo}}~}~\underline{\red{\mathbb{G}}\blue{\mathfrak{loria}}~} }}$ ✞

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