आव्यूह समीकरण `[(2,1),(3,2)].A.[(-3,2),(5,-3)]=[(1,0),(0,1)]` को संतुष्ट करता हुआ आव्यूह A ज्ञात करे ।

आव्यूह समीकरण `[(2,1),(3,2)].A.[(-3,2),(5,-3)]

1.	आव्यूह समीकरण `[(2,1),(3,2)].A.[(-3,2),(5,-3)]=[(1,0),(0,1)]` को संतुष्ट करता हुआ आव्यूह A ज्ञात करे ।
Answer» माना कि `B=[(2,1),(3,2)]" तथा "C=[(-3,2),(5,-3)]` अब `।B।=।(2,1),(3,2)।= (4 - 3) = 1 ne 0` ` ।C।=।(-3,2),(5,-3)।= (9-10) = - 1ne 0` अतः `B^(-1) "तथा " C^(-1)` का अस्तित्व है । `therefore` दिया गया आव्यूह समीकरण हो जाता है , `BAC = I_(2)` अब ` BAC = I_(2) rArr B^(-1) (BAC)C^(-1) = B^(-1) I_(2) C^(-1)` ` rArr (B^(-1) B) A(CC^(-1)) = B^(-1) (I_(2) C^(-1))` ` rArr I_(2) Al_(2) = B^(-1) V^(-1)` ` rArr A= B^(-1) C^(-1)` ...(I) B के अवयवो के सहखण्ड (cofactors ) है , ` B_(1) = 2, B_(12) = - 3, B_(21) = - 1l B_(22) = 2` ` therefore " adiB " = [(2,-3),(-1,2)] "का transpose " = [(2,-1),(-3,2)]` `therefore B^(-1) = (1)/(।B।)।"adi B"= [(2,-1),(-3,2)]" " [because ।B। = 1]` पुनः C के अवयवों के सहखण्ड (cofactors ) है , `C_(11) = - 3, C_(12) = - 5, C_(21) = - 2, C_(22) = - 3 ` `therefore "adi C " = [(-3,-5),(-2,-3)]" का transpose "= [(-3,-3),(-5,-3)]` ` therefore C^(-1) = (1)/(।C।)। "adi C" = [(3,2),(5,3)]"" [ because ।C। = - 1]` अब (1 ) से , `A = B^(-1)_C^(-1) = [(2,-1),(-3,2)][(3,2),(5,3)]=[(1,1),(1,0)]` .