Question

Sa se determine X ∈ M₂(R) , care verifica egalitatea matriceala:

a). X · (-1 2) = (5 10)
            (3 4)    (4 2)

Answer 1

$X= \left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]$
$\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right] * \left[\begin{array}{ccc}-1&2\\3&4\\\end{array}\right] = \left[\begin{array}{ccc}5&10\\4&2\\\end{array}\right]$
-a+3b=5
2a+4b=10

-c+3d=4
2c+4d=2

-a+3b=5              =>-a+3b=5
2a+4b=10|:2           a+2b=5 
5b=10 =>b=2
a+4=5 =>a=1

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