Solve system of linear equations, using matrix method, in questions 7 to 14. x-y+2z=7, 3x+4y-5z=-5, 2x-y+3z=12

Solve system of linear equations, using matrix method, in questions 7

1.	Solve system of linear equations, using matrix method, in questions 7 to 14. x-y+2z=7, 3x+4y-5z=-5, 2x-y+3z=12
Answer» Given system of equations, x-y+2z=7, 3x+4y-5z=-5, 2x-y+3z=12 `=[{:(1,-1,2),(3,4,-5),(2,-1,3):}][{:(x),(y),(z):}]=[{:(7),(-5),(12):}]rArrAX=B` `therefore" "A=[{:(1,-1,2),(3,4,-5),(2,-1,3):}]` `rArr" "\|A\|=[{:(1,-1,2),(3,4,-5),(2,-1,3):}]` =1(12-5)-(-1)(9+10)+2(-3-8) `=7+19-22=4ne0` `therefore` A is invertible. `"Now, "A_(11)=7, A_(12)=-19, A_(13)=-11` `A_(21)=1, A_(22)=-1, A_(23)=-1` `A_(31)=-3, A_(32)=11, A_(33)=7` `therefore" adjA"=[{:(7,-19,-11),(1,-10,-1),(-3,11,7):}]=[{:(7,1,-3),(-19,-1,11),(-11,-1,7):}]` `"and A"^(-1)=1/\|A\|"adj A"=1/4[{:(7,1,-3),(-19,-1,11),(-11,-1,7):}]` `"=1/4[{:(49-5-36),(-133+5+132),(-775+5+84):}]=[{:(2),(1),(3):}]` `therefore"x=2, y=1, z=3`