Question

4) Calcule x e y em:
a) $\left[\begin{array}{ccc}-3&x\\4&-1\end{array}\right] + \left[\begin{array}{ccc}y&-5\\3&1\end{array}\right] = \left[\begin{array}{ccc}8&1\\7&0\end{array}\right]$

b) $\left[\begin{array}{ccc}-4&3\\x&1\end{array}\right] +2 \left[\begin{array}{ccc}y&-3\\4&2\end{array}\right] = \left[\begin{array}{ccc}12&-3\\-1&5\end{array}\right]$

5)Se $A= \left[\begin{array}{ccc}2&7\\-1&4\end{array}\right] e B= \left[\begin{array}{ccc}3&-2\\6&0\end{array}\right]$, determine a matriz X em cada caso:
a) A + X = B
b)X + B = A
c)X - B = 2A
d)2A + X = 3B

Answer 1

4) a)
$-3+y=8 \\ y=11 \\ \\ x-5=1 \\ x=6$
b) $-4+2y=12\\2y=12+4\\2y=16\\y=8\\ \\x+2*4=-1\\x+8=-1\\x=-1-8\\x=-9$

5)
a) $\left[\begin{array}{ccc}2&7\\-1&4\end{array}\right] + \left[\begin{array}{cc}a _{11}& a_{12}\\a_{21}&a_{22}\end{array}\right] = \left[\begin{array}{cc}3&-2\\6&0\end{array}\right] \\ \left[\begin{array}{cc}2+a_{12}=3&7+a_{12}=-2\\-1+a_{21}=6&4+a_{22}=0\end{array}\right] \\ \left[\begin{array}{ccc}a_{12}=3-2&a_{12}=-2-7\\a_{21}=6+1&a_{22}=0-4\end{array}\right] \\ \left[\begin{array}{ccc}a_{12}=1&a_{12}=-9\\a_{21}=7&a_{22}=-4\end{array}\right]$
$X= \left[\begin{array}{ccc}1&-9\\7&-4\end{array}\right]$

$b) \left[\begin{array}{cc}a _{11}& a_{12}\\a_{21}&a_{22}\end{array}\right] + \left[\begin{array}{cc}3&-2\\6&0\end{array}\right] = \left[\begin{array}{cc}2&7\\-1&4\end{array}\right] \\ \left[\begin{array}{cc}a_{12}+3=2&a_{12}-2=7\\a_{21}+6=-1&a_{22}+0=4\end{array}\right] \\ \left[\begin{array}{ccc}a_{12}=-2-3&a_{12}=7+2\\a_{21}=-1-6&a_{22}=4+0\end{array}\right] \\ \left[\begin{array}{ccc}a_{12}=-5&a_{12}=9\\a_{21}=-7&a_{22}=4\end{array}\right]$
$X=\left[\begin{array}{ccc}-5&9\\-7&4\end{array}\right]$