आव्यूह के प्रतिलोम कि अवधारणा का प्रयोग कर निम्नलिखित आव्यूह समीकरण को हल करे ।
`[(1,-4),(3,-2)]X=[(-16,-6),(7,2)]` को हल करे ।

Explanation

माना कि `[(1,-4),(3,-2)] "तथा B = " [(-16,-6),(7,2)]`
अब `।A। =।(1 ,-4),(3,-2)। = - 2 + 12 = 10 ne 0`
अतः ` A^(-1)` का अस्तित्व है ।
` therefore ` दिया गया समीकरण हो जायेगा AX = B
अब `AX = B rArr X = A^(-1) B ` ...(I)
पुनः `A_(11) = a_(11) ` अर्थात 1 का cofactor ` = (-1)^(1 + 1)(-2) = 2`
` A_(12) = a_(12) ` अर्थात -4 का cofactor ` = (-1)^(1 + 2) c = - 3 `
` A_(21) = a_(21) ` अर्थात 3 का cofactor `= (-1)^(2 + 1) (-4) = 4 `
`A_(22) = a_(22)` अर्थात -3 का cofactor ` = (-1)^(2 + 2) 1 = 1 `
`therefore B= [(A_(11) , A_(12)),(A_(21),A_(22))]=[(-2,-3),(4,1)] therefore "adj A = B '"=[(-2,4),(-3,1)]`
`therefore A^(-1) = ("adj A")/(|A|) = (1)/(10) [(-2,4),(-3,1)]`
` therefore (1) "से "X = A^(1) B = (1)/(10) [(-2,4),(-3,1)][(-16,-6),(7,2)]`
`= (1)/(10) [(60,20),(55,20)]=[(6,2),((11)/(2) ,2)]`.