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Question
If A = `[(1,0,0),(2,1,0),(3,3,1)]` then find A-1 by using elementary transformation .
Solution
Consider AA-1 = I
∴ `[(1,0,0),(2,1,0),(3,3,1)]"A"^-1 = [(1,0,0),(0,1,0),(0,0,1)]`
Apply R2 → R2 - 2R1 , R3 → R3 - 3R1
∴ `[(1,0,0),(0 ,1,0),(0,3,1)]"A"^-1 = [(1,0,0),(-2,1, 0),(-3, 0,1)]`
Apply R3 → R3 - 3R2
∴ `[(1,0,0),(0,1,0),(0,0,1)]"A"^-1 = [(1,0, 0),(-2,1,0),(3,-3,1)]`
∴ IA-1 = `[(1,0,0),(-2,1,0),(3,-3,1)]`
∴ A-1 = `[(1,0,0),(-2,1,0),(3,-3,1)]`
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