Advertisements
Advertisements
प्रश्न
Find adj(adj(A)) if adj A = `[(1, 0, 1),(0, 2, 0),(-1, 0, 1)]`
उत्तर
Given adj A = `[(1, 0, 1),(0, 2, 0),(-1, 0, 1)]` to find adj(adj A)
Let adj A = B
∴ adj(adj A) = adj B
Now adj B = (Bij)T
(i.e) B = `[(1, 0, 1),(0, 2, 0),(-1, 0, 1)]`
(Bij) = `[(+|(2, 0),(0, 1)|, -|(0, 0),(-1, 1)|, +|(0, 2),(-1, 0)|),(-|(0, 1),(0, 1)|, +|(1, 1),(-1, 1)|, -|(1, 0),(-1, 0)|),(+|(0, 1),(2, 0)|, -|(1, 1),(0, 0)|, +|(1, 0),(0, 2)|)]`
= `[(+(2 - 0), -(0 - 0), +(0 + 2)),(-(0), +(1 + 1), -(0)),(+(0 - 2), -(0), +(2 - 0))]`
= `[(2, 0, 2),(0, 2, 0),(-2, 0, 2)]`
(Bij)T = `[(2, 0, -2),(0, 2, 0),(2, 0, 2)]`
(i.e) aj B = adj(adj A) = `[(2, 0, -2),(0, 2, 0),(2, 0, 2)]`
APPEARS IN
संबंधित प्रश्न
Find the adjoint of the following:
`[(-3, 4),(6,2)]`
Find the adjoint of the following:
`[(2, 3, 1),(3, 4, 1),(3, 7, 2)]`
Find the adjoint of the following:`1/3[(2, 2, 1),(-2, 1, 2),(1, -2, 2)]`
Find the inverse (if it exists) of the following:
`[(-2, 4),(1, -3)]`
Find the inverse (if it exists) of the following:
`[(5, 1, 1),(1, 5, 1),(1, 1, 5)]`
If A = `[(8, -4),(-5, 3)]`, verify that A(adj A) = (adj A)A = |A|I2
If A = `[(3, 2),(7, 5)]` and B = `[(-1, -3),(5, 2)]`, verify that (AB)–1 = B–1 A–1
If adj(A) = `[(2, -4, 2),(-3, 12, -7),(-2, 0, 2)]`, find A
If adj(A) = `[(0, -2, 0),(6, 2, -6),(-3, 0, 6)]`, find A–1
A = `[(1, tanx),(-tanx, 1)]`, show that AT A–1 = `[(cos 2x, - sin 2x),(sin 2x, cos 2x)]`
Find the matrix A for which A`[(5, 3),(-1, -2)] = [(14, 7),(7, 7)]`
Choose the correct alternative:
If A = `[(2, 0),(1, 5)]` and B = `[(1, 4),(2, 0)]` then |adj (AB)| =
Choose the correct alternative:
If + = `[(1, x, 0),(1, 3, 0),(2, 4, -2)]` is the adjoint of 3 × 3 matrix A and |A| = 4, then x is
Choose the correct alternative:
If ATA–1 is symmetric, then A2 =
Choose the correct alternative:
Which of the following is/are correct?
(i) Adjoint of a symmetric matrix is also a symmetric matrix.
(ii) Adjoint of a diagonal matrix is also a diagonal matrix.
(iii) If A is a square matrix of order n and λ is a scalar, then adj(λA) = λn adj (A).
(iv) A(adj A) = (adj A)A = |A|I
