Given `A=[{:(1 " "-1 " "1),(1 " "-2 " "-2),(2 " "1 " "3):}] and B=[{:(-4 " "4" "4),(-7 " "1 " "3),(5 " "-3 " "-1):}]`, find AB and use this result in solving the following system of equation x-y+z=4, x-2y-2z=9 2x+2y+3z=1

Given `A=[{:(1 " "-1 " "1),(1 " "-2 " "-2),(2 " "1 " "3):}] and B=[{:(

1.	Given `A=[{:(1 " "-1 " "1),(1 " "-2 " "-2),(2 " "1 " "3):}] and B=[{:(-4 " "4" "4),(-7 " "1 " "3),(5 " "-3 " "-1):}]`, find AB and use this result in solving the following system of equation x-y+z=4, x-2y-2z=9 2x+2y+3z=1
Answer» The given equation are `x-y+z=4," " ...(i)` `x-2y-2z=9" " ...(ii)` `2x+2y+3z=1" " ...(iii)` `Let A=[{:(1 " "-1 " "1),(1 " "-2 " "-2),(2 " "1 " "3):}],X=[{:(x),(y),(z):}]and C=[{:(4),(9),(1):}]` Then the given system of equations is AX=C. `Now , AB=[{:(1 " "-1 " "1),(1 " "-2 " "-2),(2 " "1 " "3):}][{:(-4 " "4" "4),(-7 " "1 " "3),(5 " "-3 " "-1):}]` `=[{:(-4+7+5 " "4-1-3 " "4-3-1),(-4+14-10 " "4-2+6 " "4-6+2),(-8-7+15 " "8+1-9 " "8+3-3):}]=[{:(8 " "0 " "0),(0 " "8 " "0),(0 " "0 " "8):}]=8I` `rArrA.(1/8B)=I` `rArr A^(-1)=1/8B=1/8[{:(-4 " "4" "4),(-7 " "1 " "3),(5 " "-3 " "-1):}]` Now , AX=C `rArr X=A^(-1)C` `rArr[{:(x),(y),(z):}]=1/8.[{:(-4 " "4" "4),(-7 " "1 " "3),(5 " "-3 " "-1):}][{:(4),(9),(1):}]` `1/8.[{:(-16+36+4),(-28+9+3),(20-27-1):}]=1/8.[{:(24),(-16),(-8):}]=[{:(3),(-2),(-1):}]` `rArr x=3, y=-2 and z=-1` Hence , x=3, y=-2 and z=-1