निम्नलिखित समीकरण निकाय को हल कीजिए।
`2/x+3/y+10/z=4`
`4/x-6/y+5/z=1`
`6/x+9/y-20/z=2`

Explanation

माना `1/x=p,1/y=q,1/z=r`
`:.` दिया गया समीकरण निकाय
`2p+3q+10r=4` ltbgt `4p-6q+5r=1`
`6p+9q-20r=2`
`implies[(2,3,10),(4,-6,5),(6,9,-20)][(p),(q),(r)]=[(4),(1),(2)]impliesAX=B`…………..1
`:.A[(2,3,10),(4,-6,5),(6,9,-20)]`
`=2(120-45)-3(-80-30)+10(36+36)`
`=150+330+720=1200!=0`
`impliesA` व्‍युत्‍क्रमणीय है।
`A_(11)=75,A_(12)=110,A_(13)=72`
`=A_(21)=150,A_(22)=100,A_(23)=0`
`A_(31)=75,A_(32)=30,A_(33)=-24`
`:.adjA=[(75,110,72),(150,-100,0),(75,30,-24)]`
`=[(75,150,75),(110,-100,30),(72,0,-24)]`
तथा `A^(-1)=1/(|A|).adjA=1/1200[(75,150,75),(110,-100,30),(72,0,-24)]`
समीकरण 1 से `AX=BimpliesX=A^(-1)B`
`implies[(p),(q),(r)]=1/1200[(75,150,75),(110-100,30),(72,0,-24)][(4),(1),(2)]`
`=1/1200[(300+150+150),(440-100+60),(288+0-48)]=[(1/2),(1/3),(1/5)]`
`implies p=1/2,q=1/3,r=1/5`
`implies1/x=1/2,1/y=1/3,1/z=1/5`
`impliesx=2,y=3,z=5`