Question

 
meeeeeeeee ajudemmmmmmmm    Matrizes!!

Determine os valores de x, y, z de modo que que

4 [ x 2] - [y 6] = [3 2]
   [-2 1]    [5 y]    [7 0]

Obrigada!

Answer 1

Olá,

só fazer a subtração algébrica das matrizes, lembrando que na multiplicação de um número real por uma matriz segue que..

$x\cdot \left(\begin{array}{ccc}a&b\\c&d\\\end{array}\right)\Rightarrow \left(\begin{array}{ccc}a\cdot x&b\cdot x\\c\cdot x&d\cdot x\\\end{array}\right)\Rightarrow \left(\begin{array}{ccc}ax&bx\\cx&dx\\\end{array}\right)$

E lembrar da igualdade entre matrizes..

$4\cdot \left(\begin{array}{ccc}x&2\\-2&1\\\end{array}\right)- \left(\begin{array}{ccc}y&6\\5&y\\\end{array}\right)= \left(\begin{array}{ccc}3&2\\7&0\\\end{array}\right)\\\\ \Rightarrow \left(\begin{array}{ccc}4\cdot x&4\cdot2\\4\cdot(-2)&4\cdot1\\\end{array}\right)- \left(\begin{array}{ccc}y&6\\5&y\\\end{array}\right)= \left(\begin{array}{ccc}3&2\\7&0\\\end{array}\right)$

$\Rightarrow \left(\begin{array}{ccc}4x&8\\-8&4\\\end{array}\right)- \left(\begin{array}{ccc}y&6\\5&y\\\end{array}\right)= \left(\begin{array}{ccc}3&2\\7&0\\\end{array}\right)\\\\ \Rightarrow \left(\begin{array}{ccc}4x-y&8-6\\-8-5&4-y\\\end{array}\right)= \left(\begin{array}{ccc}3&2\\7&0\\\end{array}\right)\\\\\\ \begin{cases}4x-y=3~~(i)\\ 4-y=0~~(ii)\end{cases}\\\\\\ y=4~~~~~~4x-y=3\\ ~~~~~~~~~~~~~~4x-4=3\\ ~~~~~~~~~~~~~~~4x=7\\\\ ~~~~~~~~~~~~~~~~x= \dfrac{7}{4}$


Tenha ótimos estudos ;D