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प्रश्न
If adj(A) = `[(2, -4, 2),(-3, 12, -7),(-2, 0, 2)]`, find A
उत्तर
adj(A) = `[(2, -4, 2),(-3, 12, -7),(-2, 0, 2)]`
A = `+- 1/sqrt(+"adj A"|)` adj (adj A)
|adj (A)| = 2(24 – 0) + 4(– 6 – 14) + 2(0 + 24)
= 48 – 80 + 48
= 16
adj (adj A) = `[(+|(12, - 7),(0, 2)|, -|(-3, - 7),(-2, 2)|, +|(-3, 12),(-2, 0)|),(-|(-4, 2),(0, 2)|, +|(2, 2),(-2, 2)|, -|(2, -4),(-2, 0)|),(+|(-4, 2),(12, -7)|, -|(2, 2),(-3, -7)|, +|(2, -4),(-3, 12)|)]^"T"`
= `[(+(24 - 0), -(-6 - 14), +(0 + 24)), (-(- 8 - 0), +(4 + 4), -(0 - 8)),(+(28 - 24), -(- 14 + 6), +(24 - 12))]^"T"`
= `[(24, 20, 24),(8, 8, 8),(4, 8, 12)]^"T"`
adj (adj A) = `[(24, 8, 4),(20, 8, 8),(4, 8, 12)]`
= `4[(6, 2, 1),(5, 2, 2),(6, 2, 3)]`
`sqrt(|"adj A"|) = sqrt(16)` = 4
A = `+- (1/4) 4[(6, 2, 1),(5, 2, 2),(6, 2, 3)]`
= `+- [(6, 2, 1),(5, 2, 2),(6, 2, 3)]`
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