The system 2 x+3 y+z=5,3 x+y+5 z=7 and x+4 y-2 z=3 has

Step-by-step solution

Given, 2 x+3 y+z=5 , aligned & 3 x+y+5 z=7, & x+4 y-2 z=3 aligned The given system can be written as A X=B , where A= [ array ccc 2 & 3 & 1 3 & 1 & 5 1 & 4 & -2 array ], X= [ array l x y z array ], B= [ array l 5 7 3 array ]|A|= | array ccc 2 & 3 & 1 3 & 1 & 5 1 & 4 & -2 array | aligned & =2(-2-20)-3(-6-5)+1(12-1) & =2(-22)-3(-11)+1(11) & =-44+33+11=0 & |A|=0 aligned As |A|=0 , this system can have no solution (or) infinitely many solutions. So we check ( adj A) B . adj A= [ array ccc -22 & 10 & 14 11 & -5 & -7 11