आव्यूह `A={:[(1,1,1),(1,-1,1),(2,1,-1)]:}` का व्युत्क्रम ज्ञात कीजिए।

Explanation

सर्वप्रथम हम इसको समीकरण रूप में निम्न प्रकार लिखते है-
A=IA
`{:[(1,1,1),(1,-1,1),(2,1,-1)]=[(1,0,0),(0,1,0),(0,0,1)]:}A`
`{:[(1,0,-2),(1,-1,1),(2,1,-1)]=[(-1,0,1),(0,1,0),(0,0,1)]:}A," "R_(1)toR_(3)-R_(1)`
`{:[(1,0,-2),(1,-1,3),(0,1,3)]=[(-1,0,1),(1,1,-1),(2,0,-1)]:}A," "R_(2)toR_(2)-R_(1)" तथा "R_(3)toR_(3)-2R_(1)`
`{:[(1,0,-2),(1,-1,3),(0,0,6)]=[(-1,0,1),(1,1,-1),(3,1,-2)]:}A," "R_(3)toR_(2)+R_(3)`
`{:[(1,0,-2),(0,-1,3),(0,0,1)]=[(-1,0,1),(1,1,-1),(1//2,1//6,-1//3)]:}A," "R_(3)to(1)/(6)R_(3)`
`{:[(1,0,0),(0,-1,0),(0,0,1)]=[(0,1//3,1//3),(-1//2,1//2,0),(1//2,1//6,-1//3)]:}A," "R_(1)toR_(1)+2R_(3)" तथा "R_(2)toR_(2)-3R_(3)`
`{:[(1,0,0),(0,1,0),(0,0,1)]=[(0,1//3,1//3),(+1//2,-1//2,0),(1//2,1//6,-1//3)]:}A," "R_(2)to-R_(2)`
अतः `A^(-1)={:[(0,1//3,1//3),(1//2,-1//2,0),(1//2,1//6,-1//3)]:}`