Examine the consistency of the system of equations`3x y 2z = 2``2y z = 1``3x 5y = 3`

Explanation

3x-y-2z=2
2y-z=-1
3x-5y=3
`rArr" "[{:(3,-1,-2),(0,2,-1),(3,-5,0):}][{:(x),(y),(z):}]=[{:(2),(-1),(3):}]rArrAX=B`
`therefore" "A=[{:(3,-1,-2),(0,2,-1),(3,-5,0):}]`
`rArr" "|A|=[{:(3,-1,-2),(0,2,-1),(3,-5,0):}]=3(0-5)-0+3(I+4)`
= -15+15=0
`therefore` A is non-invertible.
`"Now, "A_(11)=-5, A_(12)=-3, A_(13)=-6`
`A_(21)=10, A_(22)=6, A_(23)=12`
`A_(31)=5, A_(32)=3, A_(33)=6`
`rArr" adj A="[{:(-5,-3,-6),(10,6,12),(5,3,6):}]=[{:(-5,10,5),(-3,6,3),(-6,12,6):}]`
`therefore" (adj A)B="[{:(-5,-3,-6),(10,6,12),(5,3,6):}]=[{:(2),(-1),(3):}]`
`="[{:(-10,-10,+15),(-6,-6,+9),(-12,-12,+18):}]=[{:(-5),(-3),(-6):}]ne0`
`rArr` Given system of equations is inveonsistent.