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प्रश्न
Find the inverse of the matrices (if it exists).
`[(1,0,0),(3,3,0),(5,2,-1)]`
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उत्तर
A = `[(1,0,0),(3,3,0),(5,2,-1)]`
|A| = `|(1,0,0),(3,3,0),(5,2,-1)|`
= −1[−3 − 0]
= 1 × (−3)
= −3
A11 = `(-1)^(1 + 1) |(3,0),(2,-1)|`
= (−1)2 [−3 − 0]
= 1 × (−3)
= −3
A12 = `(-1)^(1 + 2) |(3,0),(5,-1)|`
= (−1)3 [−3 − 0]
= −1 × (−3)
= 3
A13 = `(-1)^(1 + 3) |(3,3),(5,2)|`
= (−1)4 [6 − 15]
= 1 × (−9)
= −9
A21 = `(-1)^(2 + 1) |(0,0),(2,-1)|`
= (−1)3 [0 − 0]
= 0
A22 = `(-1)^(2 + 2) |(1,0),(5,-1)|`
= (−1)4 [−1 − 0]
= 1 × (−1)
= −1
A23 = `(-1)^(2 + 3) |(1,0),(5,2)|`
= (−1)5 [2 − 0]
= −1 × 2
= −2
A31 = `(-1)^(3 + 1) |(0,0),(3,0)|`
= (−1)4 [0 − 0]
= 0
A32 = `(-1)^(3 + 2) |(1,0),(3,3)|`
= (−1)5 [0 − 0]
= 0
A33 = `(-1)^(3 + 3) |(1,0),(3,3)|`
= (−1)6 [3 − 0]
= 1 × 3
= 3
∴ adj A = `[(-3,3,-9),(0,-1,-2),(0,0,3)] = [(-3,0,0),(3,-1,0),(-9,-2,3)]`
A−1 = `1/|A|` adj A
= `1/-3 [(-3,0,0),(3,-1,0),(-9,-2,3)]`
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