Use product `[1-1 2 0 2-3 3-2 4]\ \ [-2 0 1 9 2-3 6 1-2]` to solve the system of equation: `x-y+2z=1` `2y-3z=1` `3x-2y+4z=2`

Explanation

`"Let "A=[{:(1,-1,2),(0,2,-3),(3,-2,4):}]" and "B=[{:(-2,0,1),(9,2,-3),(6,1,-2):}]`
`therefore" AB"=[{:(1,-1,2),(0,2,-3),(3,-2,4):}][{:(-2,0,1),(9,2,-3),(6,1,-2):}]`
`=[{:(-2-9+12,0-2+2,1+3-4),(0+18-18,0+4-3,0-6+6),(-6-18+24,0-4+4,3+6-8):}]`
`=[{:(1,0,0),(0,1,0),(0,0,1):}]=I`
write the given equations in matrix form
`=[{:(1,-1,2),(0,2,-3),(3,-2,4):}][{:(x),(y),(z):}]=[{:(1),(1),(2):}]`
AX=C
`rArr" "X=A^(-1)C=BC`
`=[{:(x),(y),(z):}]=[{:(-2,0,1),(9,2,-3),(6,1,-2):}][{:(1),(1),(2):}]=[{:(-2,+0,+2),(9,+2,-6),(6,+1,-4):}]=[{:(0),(5),(3):}]`
`therefore" "x=0, y=5, z=3`.