1.

सिद्ध कीजिए कि `Delta=|{:(a,a+b,a+b+c),(2a,3a+2b,4a+3b+2c),(3a,6a+3b,10+6b+3c):}|=a^(3).`

Answer» `Delta=|{:(a,a+b,a+b+c),(2a,3a+2b,4a+3b+2c),(3a,6a+3b,10+6b+3c):}|=a^(3).`
`=|{:(a,a+b,a+b+c),(0,a,2a+b),(3a,6a+3b,10a+6b+3c):}|,R_(2)toR_(2)-2R_(1)`के प्रयोग से
`|{:(a,a+b,a+b+c),(0,a,2a+b),( 0, 3a,7a+3b):}|,R_(3)to R_(3)-3R_(1)`के प्रयोग से
`C_(1)` के अनुदिश प्रयास करने पर,
`Delta=a[a(7a+3b)-3a(2a+b)]`
`=a(7a^(2)+3ab-6a^(2)-3ab)]`
`=a(a^(2))=a^(3).`


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