Use matrix method to show that the following system of equation is inconsistent 3x-y+2z=3 2x+y+3z=5 x-2y-z=1

Use matrix method to show that the following system of equation is inc

1.	Use matrix method to show that the following system of equation is inconsistent 3x-y+2z=3 2x+y+3z=5 x-2y-z=1
Answer» Let us take `A=[{:(3 " "-1 " "2),(2 " "1 " "3),(1 " -2 "-1):}] , X=[{:(x),(y),(z):}] and B=[{:(3),(5),(1):}]` The given system in matrix from is AX =B Now `\|A\|=[{:(3 " "-1 " "2),(2 " "1 " "3),(1 " -2 "-1):}]` =3(-1+6)+1.(-2-3)+2.(-4-1) =(15-5-10)=0 So the system will be inconsistent of \|A\| are `M_(11)=5,M_(12)=-5,M_(13)=-5` `M_(21)=5,M_(22)=-5,M_(23)=-5` `M_(31)=-5,M_(32)=5,M_(33)=5` So the confactors of the elements of \|A\| are `A_(11)=5,A_(12)=-5,A_(13)=-5` `A_(21)=5,A_(22)=-5,A_(23)=-5` `A_(31)=-5,A_(32)=5,A_(33)=5` `therefore (adjA)==[{:(5 " "5 " "-5),(-5 " "-5 " "5),(-5 " -5 " 5):}]= =[{:(5 " "-5 " "-5),(5 " "-5 " "-5),(-5 " 5 " 5):}]` `rArr (adjA)B =[{:(5 " "-5 " "-5),(5 " "-5 " "-5),(-5 " 5 " 5):}]` `[{:(3),(5),(1):}]` `=[{:(5.3+(-5).5+(-5).1),(5.3+(-5).5+(-5).1),((-5).3+5.5+5.1):}]=[{:(15-25-5),(15-25-5),(-15+25+5):}]` `=[{:(-15),(-15),(15):}]neO` Thus \|A\|=0and (adjA)B` ne ` O. ltbrrgt Hence the given system of equation is inconsistent