निम्नलिखित समीकरण निकाय को आव्यूह विधि से हल कीजिए।
`2x+y+z=1,x-2y-z=3/2,3y-5z=9`

Explanation

दिया समीकरण निकाय
`2x+y+z=1`
`x-2y-z=3/2`
`3y-5z=9`
`implies[(2,1,1),(1,-2,-1),(0,3,-5)][(x),(y),(z)]=[(1),(3/2),(9)]impliesAX=B`……………1
`impliesA=[(2,1,1),(1,-2,-1),(0,3,-5)]`
`implies|A|=[(2,1,1),(1,-2,-1),(0,3,-5)][(x),(y),(z)]=[(1),(3/2),(9)]impliesAX=B`.............1
`A=[(2,1,1),(1,-2,-1),(0,3,-5)]`
`implies |A|=|(2,1,1),(1,-2,-1),(0,3,-5)|`
`=2(10+3)-1(-5-0)+1(3-0)`
`=26+5+3=34!=0`
`:.A` व्‍युत्‍क्रमणीय है
अब `A_(11)=13,A_(12)=5,A_(13)=3`
`A_(21)=8,A_(22)=-10,A_(23)=-6`
`A_(31)=1, A_(32)=3,A_(33)=-5`
`:.adjA=[(13,5,3),(8,-10,-6),(1,3,-5)]'=[(13,8,1),(5,-10,3),(3,-6,-5)]`
तथा `A^(-1)=1/(|A|).adjA=1/34[(13,8,1),(5,-10,3),(3,-6,-5)]`
समीकरण 1 `AX=BimpliesX=A^(-1)B`
`implies[(x),(y),(z)]=1/34[(13,8,1),(5,-10,3),(3,-6,-5)][(1),(3/2),(9)]`
`=1/34[(13+12+9),(5-15+27),(3-9-45)]=[(1),(1/2),(-3/2)]`
`:.x=1,y=-1/2,z=-3/2`