Question

Calcule o valor de x e y : (MATRIZES)

a)
  
     |-3 X|    +  |Y - 5 |    =  |8  1|
    | 4 -1|       | 3  1  |        |7 0 |

B) |-4 3|  +2  |Y -3 |  =  |12  -3 |
    |X  1|        |4  2  |     | -1 5  |


C) |0  1 |  -3  |X -2 |  =  |9  8|
    | 1 Y |      |3  0 |      |-11 4 |

Answer 1

Olá, Wesley.

$a)\, \left[\begin{array}{cc}-3&x\\4&-1&\end{array}\right]+ \left[\begin{array}{ccc}y&-5\\3&1\end{array}\right]= \left[\begin{array}{cc}8&1\\7&0\end{array}\right] \Rightarrow\begin{cases}x-5=1\Rightarrow\boxed{x=6}\\-3+y=8\Rightarrow\boxed{y=11}\end{cases}$

$b)\, \left[\begin{array}{cc}-4&3\\x&1\end{array}\right]+2\left[\begin{array}{ccc}y&-3\\4&2\end{array}\right]= \left[\begin{array}{cc}12&-3\\-1&5\end{array}\right] \Rightarrow\\\\\begin{cases}-4+2y=12\Rightarrow2y=16\Rightarrow\boxed{y=8}\\x+8=-1\Rightarrow\boxed{x=-9}\end{cases}$

$c)\, \left[\begin{array}{cc}0&1\\1&y\end{array}\right]-3\left[\begin{array}{cc}x&-2\\3&0\end{array}\right]= \left[\begin{array}{cc}9&8\\-11&4\end{array}\right] \Rightarrow\\\\\begin{cases}0-3x=9\Rightarrow\boxed{x=-3}\\y-0=4\Rightarrow\boxed{y=4}\end{cases}$

Answer 2

a) Se $\left[\begin{array}{cc}-3&x\\4&-1\end{array}\right]+\left[\begin{array}{cc}y&-5\\3&1\end{array}\right]=\left[\begin{array}{cc}8&1\\7&0\end{array}\right]$, então:

$-3+y=8$

$y=11$


$x-5=1$

$x=6$

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

$-4+2y=12$

$2y=16$

$y=8$

$x+8=-1$

$x=-9$

c) Se $\left[\begin{array}{cc}0&1\\1&y\end{array}\right]-3\left[\begin{array}{cc}x&-2\\3&0\end{array}\right]=\left[\begin{array}{cc}9&8\\-11&4\end{array}\right]$, então:

$0-3x=9$

$-3x=9$

$x=-3$

$y-3\cdot0=4$

$y=4$