प्रारम्भिक पंक्ति रूपान्तरण से `A=[{:(5,-1),(1," "1):}]` का व्यूत्क्रम ज्ञात कीजिए ।

Explanation

हम जानते हैं कि A = IA
`rArr[{:(5,-1),(1,1):}]=[{:(1,0),(0,1):}]A`
`rArr[{:(1,(1)/(5)),(1,1):}]=[{:((1)/(5),0),(0,1):}]A" " R_(1)to(1)/(5)R_(1)`
`rArr[{:(1,-(1)/(5)),(0,(6)/(5)):}]=[{:((1)/(5),0),(-(1)/(5),1):}]A" " R_(2)toR_(2)-R_(1)`
`rArr[{:(1,-(1)/(5)),(0,1):}]=[{:((1)/(5),0),(-(1)/(6),(5)/(6)):}]A " " R_(2)to(5)/(6)R_(2)`
`rArr[{:(1,0),(0,1):}]=[{:((1)/(6),(1)/(6)),(-(1)/(6),(5)/(6)):}]A " " R_(1)toR_(1)+(1)/(5)R_(2)`
`rArrA^(-1)=[{:((1)/(6),(1)/(6)),(-(1)/(6),(5)/(6)):}]=(1)/(6)[{:(1,1),(-1,5):}]`