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If A = [30003003], then |A| |adj A| = - Mathematics and Statistics

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प्रश्न

If A = `[(3, 0, 0),(0, 3, 0),(0, 0, 3)]`, then |A| |adj A| = ______

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MCQ
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उत्तर

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अध्याय 1.2: Matrics - MCQ

संबंधित प्रश्न

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adj (A) = `[("____", "____", "____"),("____", "____","____"),("____","____","____")]`

A.adj (A) = `[(2, 0, -1),(5, 1, 0),(0, 1, 3)] [("( )", -1, 1), (-15, "( )", -5),("( )", -2, "( )")] = [(1, 0, "( )"),("( )", "( )", "( )"),(0, "( )", "( )")]` = |A|I


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If A = `[(4, 3, 2),(-1, 2, 0)]`, B = `[(1, 2),(-1, 0),(1, -2)]`

Find (AB)–1 by adjoint method.

Solution:

AB = `[(4, 3, 2),(-1, 2, 0)] [(1, 2),(-1, 0),(1, -2)]`

AB = [  ]

|AB| =  `square`

M11 = –2  ∴ A11 = (–1)1+1 . (–2) = –2

M12 = –3     A12 = (–1)1+2 . (–3) = 3

M21 = 4       A21 = (–1)2+1 . (4) = –4

M22 = 3       A22 = (–1)2+2 . (3) = 3

Cofactor Matrix [Aij] = `[(-2, 3),(-4, 3)]`

adj (A) = [  ]

A–1 = `1/|A| . adj(A)`

A–1 = `square`


Find the inverse of the matrix `[(1, 1, 1),(1, 2, 3),(3, 2, 2)]` by elementary column transformation.


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