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प्रश्न
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
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उत्तर
11
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संबंधित प्रश्न
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:
`[(5, 1, 1),(1, 5, 1),(1, 1, 5)]`
Find the inverse (if it exists) of the following:
`[(2, 3, 1),(3, 4, 1),(3, 7, 2)]`
If A = `[(5, 3),(-1, -2)]`, show that A2 – 3A – 7I2 = O2. Hence find A–1
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
Find adj(adj(A)) if adj A = `[(1, 0, 1),(0, 2, 0),(-1, 0, 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 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 = `[(1, -2),(1, 4)] = [(6, 0),(0, 6)]`, then 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 A B, and C are invertible matrices of some order, then which one of the following is not true?
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
Choose the correct alternative:
If A = `[(3, -3, 4),(2, -3, 4),(0, -1, 1)]`, then adj(adj A) is
