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प्रश्न
Find the inverse of the following matrix (if they exist):
`((1,-1),(2,3))`
उत्तर
Let A = `((1,-1),(2,3))`
∴ |A| = `|(1,-1),(2,3)| = 3 + 2 = 5 ≠ 0`
∴ A-1 exists.
Consider AA-1 = I
∴ `((1,-1),(2,3)) "A"^-1 = ((1,0),(0,1))`
By R2 - 2R1, we get,
`((1,-1),(0,5)) "A"^-1 = ((1,0),(-2,1))`
By `(1/5) "R"_2`, we get,
`((1,-1),(0,1)) "A"^-1 = ((1,0),(-2/5,1/5))`
By R1 + R2, we get,
`((1,0),(0,1)) "A"^-1 = ((3/5,1/5),(-2/5,1/5))`
∴ A-1 = `1/5((3,1),(-2,1))`
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