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Question
Find the inverse of the following matrix (if they exist):
`[(2,1),(7,4)]`
Solution
Let A = `[(2,1),(7,4)]`
∴ |A| = `|(2,1),(7,4)| = 8 - 7 = 1 ne 0`
∴ A-1 exists.
Consider AA-1 = I
∴ `[(2,1),(7,4)] "A"^-1 = [(1,0),(0,1)]`
By R1 → R1 - `1/7`R2 we get,
`[(1,3/7),(7,4)] "A"^-1 = [(1,(-1)/7),(0,1)]`
By R2 → R2 - 7R1 we get,
`[(1,3/7),(0,1)] "A"^-1 = [(1,(-1)/7),(-7,2)]`
By R1 → R1 - `3/7`R2
`[(1,0),(0,1)] "A"^-1 = [(4,-1),(-7,2)]`
∴ `"A"^-1 = [(4,-1),(-7,2)]`
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