Tamil Nadu Board of Secondary EducationHSC Arts Class 12

Find the inverse (if it exists) of the following: [511151115] - Mathematics

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Sum

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

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

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Solution

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

|A| = 5(25 – 1) – (5 – 1) + 1(1 – 5)

= 5(24) – 1(4) + 1(– 4)

= 120 – 4 – 4

= 122 ≠ 0.A1 exists

adj A = `[(+|(5, 1),(1, 5)|, -|(1, 1),(1, 5)|, +|(1, 5),(1, 1)|),(-|(1, 1),(1, 5)|, +|(5, 1),(1, 5)|, -|(5, 1),(1, 1)|),(+|(1, 1),(5, 1)|, -|(5, 1),(1, 1)|, +|(5, 1),(1, 5)|)]^"T"`

= `[(+(25 - 1), (5 - 1), +(1 - 5)),(-(5 - 1), +(25 - 1), -(5 - 1)),(+(1 - 5), -(5 - 1), +(25 - 1))]^"T"`

= `[(24, -4, -4),(-4, 24, -4),(4, -4, 24)]^"T"`

adj A = `[(24, -4, -4),(-4, 24, -4),(4, -4, 24)]`

`"A"^-1 = 1/|"A"|`

adj A = `1/112 [(24, -4, -4),(-4, 24, -4),(4, -4, 24)]`

= `1/28 [(6, -1, -1),(-1, 6, -1),(-1, -1, 6)]`  

Concept: Inverse of a Non-singular Square Matrix
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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 2. (ii) | Page 15
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