प्रारंभिक रूपांतरण का प्रयोग करते हुए निम्न आव्यूह का प्रतिलोम ज्ञात कीजिए।
`[(1,3,-2),(-3,0,-5),(2,5,0)]`

Explanation

माना `A=[(1,3,-2),(-3,0,-5),(2,5,0)]`
`A^(-1)` ज्ञात करने के लिए हम पंक्ति रूपांतरण लगते हैं।
अब `A=I_(3)A`
`[(1,3,-2),(-3,0,-5),(2,5,0)]=[(1,0,0),(0,1,0),(0,0,1)]A`
`[(1,3,-2),(0,9,-11),(0,-1,4)]=[(1,0,0),(3,1,0),(-2,0,1)]A`
`(R_(2) rarr R_(2) +3R_(1), R_(3) rarr R_(3)-2R_(1))`
`[(1,3,-2),(0,1,21),(0,-1,4)]=[(1,0,0),(-13,1,8),(-2,0,1)]A`
`(R_(2)rarr R_(2) +8R_(3))`
`[[(1,0,-65),(0,1,21),(0,0,25)]=[(40,-3,-24),(-13,1,8),(-15,1,9)]A (R_(1) rarr R_(1)-3R_(2), R_(3) rarr R_(3)+R_(2))`
`[(1,0,-65),(0,1,21),(0,0,1)]=[(40,-3,-24),(-13,1,8),((-3)/5,1/25,9/25)] A (R_(3) rarr 1/25 R_(3))`
`[(1,0,0),(0,1,0),(0,0,1)]=[(1,(-2)/5,(-3)/5),((-2)/5,4/25,11/25),((-3)/5,1/25,9/25)] A(R_(1) rarr R_(1) +65 R_(3), R_(2) rarr R_(2) -21 R_(3))`
`I_(3)=BA` जहाँ `B=[(+1,(-2)/5,(-3)/5),((-2)/5,4/25,11/25),((-3)/5,1/25,9/25)]=A^(-1)`