Question

1) Escreva as matrizes:
a) A= (aij) 3×2 tal que aij= i+j
b) A= (aij) 2×3 tal que aij= i-j
c) B= (bij) 2×2 de modo que bij= 2i-j

2) Fadas as matrizes A e B | A3×3=
[ 1 -1 9 [ -1 1 -9
7 14 -8 ; B3×3= -7 -14 8
0 -5 -5 ] 0 5 5 ]
Calcule o que se pede:
a) A+B
b) A-B
c) 4.A
d) -7.B

Answer 1

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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, Yuri, como tens passado nestes tempos de quarentena⁉ E os estudos à distância, como vão⁉ Espero que bem❗ Acompanhe a resolução abaixo. ✌

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1)Ⓐ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\large\gray{\boxed{\rm\blue{ a_{ij} = 1 \cdot i + 1 \cdot j }}}$

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☔ Nossa matriz portanto será da forma

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

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$\large\green{\boxed{\blue{\sf\red{1)~A)}~~~\sf\large\blue{A_{3,2}=\left[\begin{array}{cc}2&3\\\\3&4\\\\4&5\\\end{array}\right]}~~~}}}$ ✅

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

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$\large\gray{\boxed{\rm\blue{ a_{ij} = 1 \cdot i + (-1) \cdot j }}}$

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☔ Nossa matriz portanto será da forma

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$\sf\blue{A_{2,3}=\left[\begin{array}{ccc}1 \cdot 1 + (-1) \cdot 1&1 \cdot 1 + (-1) \cdot 2&1 \cdot 1 + (-1) \cdot 3\\\\1 \cdot 2 + (-1) \cdot 1&1 \cdot 2 + (-1) \cdot 2&1 \cdot 2 + (-1) \cdot 3\\\end{array}\right]}$

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$\large\green{\boxed{\blue{\sf\red{1)~B)}~~~\sf\large\blue{A_{2,3}=\left[\begin{array}{ccc}0&-1&-2\\\\1&0&-1\\\end{array}\right]}~~~}}}$ ✅

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

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$\large\gray{\boxed{\rm\blue{ b_{ij} = 2 \cdot i + (-1) \cdot j }}}$

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☔ Nossa matriz portanto será da forma

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$\sf\blue{B_{2,2}=\left[\begin{array}{cc}2 \cdot 1 + (-1) \cdot 1&2 \cdot 1 + (-1) \cdot 2\\\\2 \cdot 2 + (-1) \cdot 1&2 \cdot 2 + (-1) \cdot 2\\\end{array}\right]}$

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$\large\green{\boxed{\blue{\sf\red{1)~C)}~~~\sf\large\blue{B_{2,2}=\left[\begin{array}{cc}1&0\\\\3&2\\\end{array}\right]}~~~}}}$ ✅

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

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$\sf\large\blue{A_{3,3} = \left[\begin{array}{ccc}1&-1&9\\\\-1&1&-9\\\\7&14&-8\\\end{array}\right]}$

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$\sf\large\blue{B_{3,3} = \left[\begin{array}{ccc}-7&-14&8\\\\0&-5&-5\\\\0&5&5\\\end{array}\right]}$

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☔ Considerando que ambas tem as mesmas dimensões então a soma e a subtração poderão ser feitas.

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

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$\sf\blue{(A+B)_{3,3} = \left[\begin{array}{ccc}1+(-7)&-1+(-14)&9+8\\\\-1+0&1+(-5)&-9+(-5)\\\\7+0&14+5&-8+5\\\end{array}\right]}$

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$\large\green{\boxed{\blue{\sf\red{2)~A)}~~~(A+B)_{3,3} = \left[\begin{array}{ccc}-6&-15&17\\\\-1&-4&-14\\\\7&19&-3\\\end{array}\right]~~~}}}$ ✅

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

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$\sf\blue{(A-B)_{3,3}=\left[\begin{array}{ccc}1-(-7)&-1-(-14)&9-8\\\\-1-0&1-(-5)&-9-(-5)\\\\7-0&14-5&-8-5\\\end{array}\right]}$

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$\large\green{\boxed{\blue{\sf\red{2)~B)}~~~(A-B)_{3,3}=\left[\begin{array}{ccc}8&13&1\\\\-1&6&-4\\\\7&9&-13\\\end{array}\right]~~~}}}$ ✅

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

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$\sf\blue{4 \cdot A_{3,3} = \left[\begin{array}{ccc}4 \cdot 1&4 \cdot (-1)&4 \cdot 9\\\\4 \cdot (-1)&4 \cdot 1&4 \cdot (-9)\\\\4 \cdot 7&4 \cdot 14&4 \cdot (-8)\\\end{array}\right]}$

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$\large\green{\boxed{\blue{\sf\red{2)~C)}~~~4 \cdot A_{3,3} = \left[\begin{array}{ccc}4&-4&36\\\\-4&4&-36\\\\28&56&-32\\\end{array}\right]~~~}}}$ ✅

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

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$\sf\blue{(-7) \cdot B_{3,3} = \left[\begin{array}{ccc}(-7) \cdot (-7)&(-7) \cdot (-14)&(-7) \cdot 8\\\\(-7) \cdot 0&(-7) \cdot (-5)&(-7) \cdot (-5)\\\\(-7) \cdot 0&(-7) \cdot 5&(-7) \cdot 5\\\end{array}\right]}$

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$\large\green{\boxed{\blue{\sf\red{2)~D)}~~~(-7) \cdot B_{3,3} = \left[\begin{array}{ccc}49&98&-56\\\\0&35&35\\\\0&-35&-35\\\end{array}\right]~~~}}}$ ✅

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

☕ $\bf\large\blue{Bons\ estudos.}$

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

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