Question

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24.
Sejam A=(12 1), B=(8 11) e C=(2 4)
(9 5), (3 6) e (10 7)
Determine as matrizes:

a) A+B+C
b) A-B+C
c) A-(B+C)

26.
Resolva as seguintes equações matriciais:

a) X+(4 3)=(5 0)
(1 1) (2 3)
(2 0) (7 8)

b) X-(1 4 7) = (-1 2 11)
(-2 5 -3) (-3 4 1)

c) (½ 1)+(3/2 4) = X - (-1 -3)
(0 2) (3 7) (-2 4)

Answer 1

24.
a) $A+B+C=\left[\begin{array}{cc}12&1\\9&5\end{array}\right]+\left[\begin{array}{cc}8&11\\3&6\end{array}\right]+\left[\begin{array}{cc}2&4\\10&7\end{array}\right]=\left[\begin{array}{cc}12+8+2&1+11+4\\9+3+10&5+6+7\end{array}\right]$

$A+B+C=\left[\begin{array}{cc}22&16\\22&18\end{array}\right]$    

b) $A-B+C=\left[\begin{array}{cc}12&1\\9&5\end{array}\right]-\left[\begin{array}{cc}8&11\\3&6\end{array}\right]+\left[\begin{array}{cc}2&4\\10&7\end{array}\right]=\left[\begin{array}{cc}12-8+2&1-11+4\\9-3+10&5-6+7\end{array}\right]$

$A-B+C=\left[\begin{array}{cc}6&-6\\16&6\end{array}\right]$

c) $A-(B+C)=A-B-C=\left[\begin{array}{cc}12&1\\9&5\end{array}\right]-\left[\begin{array}{cc}8&11\\3&6\end{array}\right]-\left[\begin{array}{cc}2&4\\10&7\end{array}\right]=\left[\begin{array}{cc}12-8-2&1-11-4\\9-3-10&5-6-7\end{array}\right]$

$A-(B+C)=\left[\begin{array}{cc}2&-14\\-4&-8\end{array}\right]$

26.

a) $X+\left[\begin{array}{cc}4&3\\1&1\\2&0\end{array}\right]=\left[\begin{array}{cc}5&0\\2&3\\7&8\end{array}\right]$

$X=\left[\begin{array}{cc}5&0\\2&3\\7&8\end{array}\right]-\left[\begin{array}{cc}4&3\\1&1\\2&0\end{array}\right]=\left[\begin{array}{cc}5-4&0-3\\2-1&3-1\\7-2&8-0\end{array}\right]$

$X=\left[\begin{array}{cc}1&-3\\1&2\\5&8\end{array}\right]$

b) $X-\left[\begin{array}{ccc}1&4&7\\-2&5&-3\end{array}\right]=\left[\begin{array}{ccc}-1&2&11\\-3&4&1\end{array}\right]$

$X=\left[\begin{array}{ccc}1&4&7\\-2&5&-3\end{array}\right]+\left[\begin{array}{ccc}-1&2&11\\-3&4&1\end{array}\right]=\left[\begin{array}{ccc}-1+1&2+4&11+7\\-3-2&4+5&1-3\end{array}\right]$

$X=\left[\begin{array}{ccc}0&6&18\\-5&9&-2\end{array}\right]$

c) $\left[\begin{array}{cc}\frac{1}{2}&1\\0&2\end{array}\right]+\left[\begin{array}{cc}\frac{3}{2}&4\\3&7\end{array}\right]=X-\left[\begin{array}{cc}-1&-3\\-2&4\end{array}\right]$

$\left[\begin{array}{cc}2&5\\3&9\end{array}\right]=X-\left[\begin{array}{cc}-1&-3\\-2&4\end{array}\right]$

$X=\left[\begin{array}{cc}2&5\\3&9\end{array}\right]+\left[\begin{array}{cc}-1&-3\\-2&4\end{array}\right]$

$X=\left[\begin{array}{cc}2-1&5-3\\3-2&9+4\end{array}\right]$

$X=\left[\begin{array}{cc}1&2\\1&13\end{array}\right]$