Tamil Nadu Board of Secondary EducationHSC Arts Class 12

Find the adjoint of the following:13[221-2121-22] - Mathematics

Advertisements
Advertisements
Sum

Find the adjoint of the following:`1/3[(2, 2, 1),(-2, 1, 2),(1, -2, 2)]`

Advertisements

Solution

A = `1/3[(2, 2, 1),(-2, 1, 2),(1, -2, 2)]_(3 xx 3)`

adj (kA) = `"k"^("n" - 1)` adj A 

adj A = `(1/3)^2 [(+|(1, 2),(-2, 2)|, -|(-2, 2),(1, 2)|, +|(-2, 1),(1, -2)|),(-|(2, 1),(-2, 2)|, +|(2, 1),(1, 2)|, -|(2, 2),(1, -2)|),(+|(2, 1),(1, 2)|, -|(2, 1),(-2, 2)|, +|(2, 2),(-2, 1)|)]^"T"`

= `1/9[(+(2 + 4), -(-4 - 2), +(4 - 1)),(-4(4 + 2), +(4 - 1), -(-4 - 2)),(+(4 - 1), -(4 + 2), +(2 + 4))]^"T"`

= `1/9[(6, 6, 3),(-6, 3, 6),(, -6, 6)]^"T"`

= `1/9[(6, -6, 3),(6, 3, -6),(3, 6, 6)]`

= `1/3[(2, -2, 1),(2, 1, 2),(1, 2, 2)]`

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 1.1 [Page 15]

APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 12th Mathematics Volume 1 and 2 Answers Guide
Chapter 1 Applications of Matrices and Determinants
Exercise 1.1 | Q 1. (iii) | Page 15

RELATED QUESTIONS

Find the adjoint of the following:

`[(2, 3, 1),(3, 4, 1),(3, 7, 2)]`


Find the inverse (if it exists) of the following:

`[(5, 1, 1),(1, 5, 1),(1, 1, 5)]`


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)]`


Given A = `[(1, -1),(2, 0)]`, B = `[(3, -2),(1, 1)]` and C = `[(1, 1),(2, 2)]`, find a martix X such that AXB = C


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


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:

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


Share
Notifications



      Forgot password?
Use app×