Tamil Nadu Board of Secondary EducationHSC Arts Class 12

Find the matrix A for which A[53-1-2]=[14777] - Mathematics

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Sum

Find the matrix A for which A`[(5, 3),(-1, -2)] = [(14, 7),(7, 7)]`

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Solution

Given A`[(5, 3),(-1, -2)] = [(14, 7),(7, 7)]`

Let B = `[(5, 3),(-1, -2)]`

C = `[(14, 7),(7, 7)]`

Given AB = C,

To find A:

Now AB = C

Post multiply by B–1 on both sides

ABB1 = CB1 

(i.e) A(BB1) = CB1

⇒ A(I) = CB1 

(i.e) A = CB1

To find B1:

B = `[(5, 3),(-1, -2)]`

|B| = `|(5, 3),(-1, -2)|`

= – 10 + 3

= – 7 ≠ 0

adj B = `[(-2, -3),(1, 5)]`

B= `1/|"B"|`

(adj B) = `1/(-7)[(-, -3),(1, 5)]`

= `1/7 [(2, 3),(-1, -5)]`

A = CB= `1/7 [(14, 7),(7, 7)] [(2, 3),(-1, -5)]` 

= `1/7 (7) [(2, 1),(1, 1)] (2, 3),(-1, -5)]`

= `[(2, 1),(1, 1)] [(2, 3),(-1, -5)]`

= `[(4 - 1, 6 - 5), (2 - 1, 3 - 5)]`

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

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

Concept: Inverse of a Non-singular Square Matrix
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Chapter 1: Applications of Matrices and Determinants - Exercise 1.1 [Page 16]

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 12 | Page 16

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