Question

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Answer 1

Explicação passo-a-passo:

$B=\left[\begin{array}{ccc}3&4\\-2&0\\5&3\end{array}\right]$     ;     $C=\left[\begin{array}{ccc}-1&2\\6&0\\-7&-3\end{array}\right]$     ;     $D=\left[\begin{array}{ccc}4&-1\\5&3\\6&-2\end{array}\right]$

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a) C + 2B - D

   $\left[\begin{array}{ccc}-1&2\\6&0\\-7&-3\end{array}\right]+2.\left[\begin{array}{ccc}3&4\\-2&0\\5&3\end{array}\right]-\left[\begin{array}{ccc}4&-1\\5&3\\6&-2\end{array}\right]$

   resolva a multiplicação primeiro. Multiplique o 2 com cada elemento

   da matriz

   $\left[\begin{array}{ccc}-1&2\\6&0\\-7&-3\end{array}\right]+\left[\begin{array}{ccc}2.3&2.4\\2.(-2)&2.0\\2.5&2.3\end{array}\right]-\left[\begin{array}{ccc}4&-1\\5&3\\6&-2\end{array}\right]$

   $\left[\begin{array}{ccc}-1&2\\6&0\\-7&-3\end{array}\right]+\left[\begin{array}{ccc}6&8\\-4&0\\10&6\end{array}\right]-\left[\begin{array}{ccc}4&-1\\5&3\\6&-2\end{array}\right]$

   some e subtraia os elementos das matrizes nas posições em que se

   encontram:  c₁₁ + b₁₁ - d₁₁

   $\left[\begin{array}{ccc}-1+6-4&2+8-(-1)\\6+(-4)-5&0+0-3\\-7+10-6&-3+6-(-2)\end{array}\right]=\left[\begin{array}{ccc}1&11\\-3&-3\\-3&5\end{array}\right]$

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b) 3B - D + C

   $3.\left[\begin{array}{ccc}3&4\\-2&0\\5&3\end{array}\right]-\left[\begin{array}{ccc}4&-1\\5&3\\6&-2\end{array}\right]+\left[\begin{array}{ccc}-1&2\\6&0\\-7&-3\end{array}\right]$

   resolva a multiplicação primeiro. Multiplique o 3 com cada elemento

   da matriz

   $\left[\begin{array}{ccc}3.3&3.4\\3.(-2)&3.0\\3.5&3.3\end{array}\right]-\left[\begin{array}{ccc}4&-1\\5&3\\6&-2\end{array}\right]+\left[\begin{array}{ccc}-1&2\\6&0\\-7&-3\end{array}\right]$

   $\left[\begin{array}{ccc}9&12\\-6&0\\15&9\end{array}\right]-\left[\begin{array}{ccc}4&-1\\5&3\\6&-2\end{array}\right]+\left[\begin{array}{ccc}-1&2\\6&0\\-7&-3\end{array}\right]$

   subtraia e some os elementos das matrizes nas posições em que se

   encontram: b₁₁ - d₁₁ + c₁₁

   $\left[\begin{array}{ccc}9-4+(-1)&12-(-1)+2\\-6-5+6&0-3+0\\15-6+(-7)&9-(-2)+(-3)\end{array}\right]=\left[\begin{array}{ccc}4&15\\-5&-3\\2&8\end{array}\right]$

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c) D + C - B

   $\left[\begin{array}{ccc}4&-1\\5&3\\6&-2\end{array}\right]+\left[\begin{array}{ccc}-1&2\\6&0\\-7&-3\end{array}\right]-\left[\begin{array}{ccc}3&4\\-2&0\\5&3\end{array}\right]$

   some e subtraia os elementos das matrizes nas posições em que se

   encontram: d₁₁ + c₁₁ - b₁₁

   $\left[\begin{array}{ccc}4+(-1)-3&-1+2-4\\5+6-(-2)&3+0-0\\6+(-7)-5&-2+(-3)-3\end{array}\right]=\left[\begin{array}{ccc}0&-3\\13&3\\-6&-8\end{array}\right]$

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d) 4D + B - C

   $4.\left[\begin{array}{ccc}4&-1\\5&3\\6&-2\end{array}\right]+\left[\begin{array}{ccc}3&4\\-2&0\\5&3\end{array}\right]-\left[\begin{array}{ccc}-1&2\\6&0\\-7&-3\end{array}\right]$

   resolva a multiplicação primeiro. Multiplique o 4 com cada elemento

   da matriz

   $\left[\begin{array}{ccc}4.4&4.(-1)\\4.5&4.3\\4.6&4.(-2)\end{array}\right]+\left[\begin{array}{ccc}3&4\\-2&0\\5&3\end{array}\right]-\left[\begin{array}{ccc}-1&2\\6&0\\-7&-3\end{array}\right]$

   $\left[\begin{array}{ccc}16&-4\\20&12\\24&-8\end{array}\right]+\left[\begin{array}{ccc}3&4\\-2&0\\5&3\end{array}\right]-\left[\begin{array}{ccc}-1&2\\6&0\\-7&-3\end{array}\right]$

   some e subtraia os elementos das matrizes nas posições em que se

   encontram:  d₁₁ + b₁₁ - c₁₁

   $\left[\begin{array}{ccc}16+3-(-1)&-4+4-2\\20+(-2)-6&12+0-0\\24+5-(-7)&-8+3-(-3)\end{array}\right]=\left[\begin{array}{ccc}20&-2\\12&12\\36&-2\end{array}\right]$