Question

1)Sejam as matrizes:
A= -5 1 B= -8 -4 C= -7 4 DETERMINE:
-9 -3 -9 -3. -3 5

a) 2A - (B + C)

b) 2(A - C) + 3(B - A)​

Answer 1

Explicação passo-a-passo:

a) 2A - (B + C)

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

   $\left[\begin{array}{ccc}2.(-5)&2.1\\2.(-9)&2.(-3)\\\end{array}\right]-\left[\begin{array}{ccc}-8+(-7)&-4+4\\-2+(-3)&-6+5\\\end{array}\right]$

   $\left[\begin{array}{ccc}-10&2\\-18&-6\\\end{array}\right]-\left[\begin{array}{ccc}-15&0\\-5&-1\\\end{array}\right]$

   $\left[\begin{array}{ccc}-10-(-15)&2-0\\-18-(-5)&-6-(-1)\\\end{array}\right]=\left[\begin{array}{ccc}5&2\\-13&-5\\\end{array}\right]$

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b) 2 (A - C) + 3 (B - A)

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

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

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

   $\left[\begin{array}{ccc}2.2&2.(-3)\\2.(-6)&2.(-8)\\\end{array}\right]+\left[\begin{array}{ccc}3.(-3)&3.(-5)\\3.7&3.(-3)\\\end{array}\right]$

   $\left[\begin{array}{ccc}4&-6\\-12&-16\\\end{array}\right]+\left[\begin{array}{ccc}-9&-15\\21&-9\\\end{array}\right]$

   $\left[\begin{array}{ccc}4+(-9)&-6+(-15)\\-12+21&-16+(-9)\\\end{array}\right]=\left[\begin{array}{ccc}-5&-21\\9&-25\\\end{array}\right]$