Tamil Nadu Board of Secondary EducationHSC Arts Class 12

Choose the correct alternative: Which of the following is/are correct? - Mathematics

Advertisements
Advertisements
MCQ

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

Options

  • Only (i)

  • (ii) and (iii)

  • (iii) and (iv)

  • (i), (ii) and (iv)

Advertisements

Solution

(i), (ii) and (iv)

Concept: Inverse of a Non-singular Square Matrix
  Is there an error in this question or solution?
Chapter 1: Applications of Matrices and Determinants - Exercise 1.8 [Page 50]

APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 12th Mathematics Volume 1 and 2 Answers Guide
Chapter 1 Applications of Matrices and Determinants
Exercise 1.8 | Q 20 | Page 50

RELATED QUESTIONS

Find the adjoint of the following:

`[(-3, 4),(6,2)]`


If `"F"(alpha) = [(cosalpha, 0, sinalpha),(0, 1, 0),(-sinalpha, 0, cosalpha)]`, show that `["F"(alpha)]^-1 = "F"(- alpha)`


If A = `[(5, 3),(-1, -2)]`, show that A2 – 3A – 7I2 = O2. Hence find A–1 


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 = B1 A1 


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 


Find adj(adj(A)) if adj A = `[(1, 0, 1),(0, 2, 0),(-1, 0, 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)]`


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 = `[(1, -2),(1, 4)] = [(6, 0),(0, 6)]`, then A =


Choose the correct alternative:

If A = `[(7, 3),(4, 2)]` then 9I2 – A =


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 ATA1 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


Share
Notifications



      Forgot password?
Use app×