Question

a inversa da matriz ... é a matriz

Answer 1

(-2  4) . ( a  b) = ( 1  0)
 -1  5      c   d        0  1
( -2a+4c    -2b+4d) = (1  0)
 -1a+5c      -1b+5d      0  1
$\left \{ {{-2a+4c=1} \atop {-1a+5c=0}} \right. \left \{ {{-2a+4c=1} \atop {-1a+5c=0 .(-2)}} \right. \left \{ {{-2a+4c=1} \atop {2a-10c=0}} \right.$
-6c=1
c= -1/6
-1a+5.( -1/6)=0
-1a-5/6=0
a= -5/6
$\left \{ {{-2b+4d=0} \atop {-1b+5d=1}} \right. \left \{ {{-2b+4d=0} \atop {-1b+5d=1 .(-2)}} \right. \left \{ {{-2b+4d=0} \atop {2b-10d=-2}} \right.  -6d=-2 .(-1) d=2/6 d=1/3 --b+5.1/3=1 -b+5/3=1 -b=1-5/3 -b=3-5/3 -b=-2/3 .(-1) b=2/3 [tex] \left[\begin{array}{ccc} -5/6& 2/3\\-1/6& 1/3\end{array}\right]$