Question

Ajudem por favor, preciso para amanhã! SOBRE MATRIZES.

Calcule o valor de x e y.


a) (  2    4  ) = 2 (1   2)
    (x+3 y-2)       (3   4)


b) (1   2) + ( y  4 ) = ( 4 6 )
    (x   3)    (-5  3 )    (10 6)

Answer 1

$a) \left(\begin{array}{ccc}2&4\\x+3&y-2\\\end{array}\right)= 2 \left(\begin{array}{ccc}1&2\\3&4\\\end{array}\right)$

Multiplicando o número real 2, pelos elementos da 2ª matriz e conservando a 1ª matriz, vem:

$\left(\begin{array}{ccc}2&4\\x+3&y-2\\\end{array}\right)= \left(\begin{array}{ccc}2*1&2*2\\2*3&2*4\\\end{array}\right)$


$\left(\begin{array}{ccc}2&4\\x+3&y-2\\\end{array}\right)= \left(\begin{array}{ccc}2&4\\6&8\\\end{array}\right)$

Igualando as incógnitas, temos;

$x+3=6~~~~~~~~~~~~~~~~~y-2=8\\\ x=6-3~~~~~~~~~~~~~~~~~y=8+2\\\ x=3~~~~~~~~~~~~~~~~~~~~~~y=10$

$\boxed{\boxed{S=(3,~10)}}$
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$b) \left(\begin{array}{ccc}1&2\\x&3\\\end{array}\right)+ \left(\begin{array}{ccc}y&4\\-5&3\\\end{array}\right)= \left(\begin{array}{ccc}4&6\\10&6\\\end{array}\right)$

Igualando as matrizes, pela soma dos elementos, vem:

$1+y=4~~~~~~~~~~~~~~x+(-5)=10\\\ y=4-1~~~~~~~~~~~~~~x-5=10\\\ y=3~~~~~~~~~~~~~~~~~~~x=10+5\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~x=15$

$\boxed{\boxed{S=(15,~3)}}$


Espero ter ajudado e tenha bons estudos :))