Tamil Nadu Board of Secondary EducationHSC Arts Class 12

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

Sum

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

#### 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
Share