Advertisements
Advertisements
Question
Find adj(adj(A)) if adj A = `[(1, 0, 1),(0, 2, 0),(-1, 0, 1)]`
Solution
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
RELATED QUESTIONS
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:
`[(2, 3, 1),(3, 4, 1),(3, 7, 2)]`
If A = `1/9[(-8, 1, 4),(4, 4, 7),(1, -8, 4)]`, prove that `"A"^-1 = "A"^"T"`
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) = `[(0, -2, 0),(6, 2, -6),(-3, 0, 6)]`, find A–1
If A = `[(0, 1, 1),(1, 0, 1),(1, 1, 0)]`, show that `"A"^-1 = 1/2("A"^2 - 3"I")`
Decrypt the received encoded message [2 – 3][20 – 4] with the encryption matrix `[(-1, -1),(2, 1)]` and the decryption matrix as its inverse, where the system of codes are described by the numbers 1 – 26 to the letters A – Z respectively, and the number 0 to a blank space
Choose the correct alternative:
If |adj(adj A)| = |A|9, then the order of the square matrix A is
Choose the correct alternative:
If A is a 3 × 3 non-singular matrix such that AAT = AT A and B = A-1AT, then BBT =
Choose the correct alternative:
If A = `[(7, 3),(4, 2)]` then 9I2 – A =
Choose the correct alternative:
If A = `[(2, 0),(1, 5)]` and B = `[(1, 4),(2, 0)]` then |adj (AB)| =
Choose the correct alternative:
If ATA–1 is symmetric, then A2 =
Choose the correct alternative:
If A is a non-singular matrix such that A–1 = `[(5, 3),(-2, -1)]`, then (AT)–1 =
Choose the correct alternative:
If A = `[(3, -3, 4),(2, -3, 4),(0, -1, 1)]`, then adj(adj A) is
