Tamil Nadu Board of Secondary EducationHSC Arts Class 12

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

Sum

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

#### 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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