Tamil Nadu Board of Secondary EducationHSC Science Class 11th

# Determine the matrices A and B if they satisfy 2A – B + [6-60-421] = 0 and A – 2B = [328-21-7] - Mathematics

Sum

Determine the matrices A and B if they satisfy 2A – B + [(6, - 6, 0),(- 4, 2, 1)] = 0 and A – 2B = [(3, 2, 8),(-2, 1, -7)]

#### Solution

2A – B + [(6, - 6, 0),(- 4, 2, 1)] = 0

A – 2B = [(3, 2, 8),(-2, 1, -7)]

2A – B = - [(6, - 6, 0),(- 4, 2, 1)] ......(1)

A – 2B = [(3, 2, 8),(-2, 1, -7)] .......(2)

(1) ⇒ 2A – B + [(6, - 6, 0),(- 4, 2, 1)]

(2) × 2 2A – 4B = [(3, 2, 8),(-2, 1, -7)]

Substuting 0 + 3B = [(6, - 6, 0),(- 4, 2, 1)] - 2[(3, 2, 8),(-2, 1, -7)]

3B = [(- 6, 6, 0),(4, - 2, -1)] - [(6, 4, 16),(-4, 2, -14)]

= [(-6 - 6, 6 - 4, 0 - 16),(4 + 4, - 2 - 2, - 1 + 14)]

3B = [(- 12, 2, - 16),(8, -4, 13)]

B = 1/3[(- 12, 2, - 16),(8, -4, 13)]

Substituting for B in equation (1)

(1) ⇒ 2"A" - 1/3 [(- 12, 2, - 6),(8, -4, 13)] = - [(6, 6, 0),(- 4, 2, 1)]

2A = 1/3[(- 1, 2, 16),(8,-4, 13)] - [(6, -6, 0),(-4, 2, 1)]

= [((-12)/3, 2/3, (-16)/3),(8/3, (-4)/3, 13/3)] - [(6, -6, 0),(-4, 2, 1)]

= [(-4 - 6, 2/3 + 6, (- 16)/3 - 0),(8/3 + 4, (-4)/3 - 2, 13/3 - 1)]

= [(- 10, (2 + 8)/3, (-16)/3),((8 + 12)/3, (-4 - 6)/3, (13 - 3)/3)]

2A = [(- 10, 20/3, (-16)/3),(20/3, (- 10)/3, 10/3)]

A = 1/2[(- 10, 0/3, (- 16)/3),(20/3, (- 10)/3, 10/3)]

A = [(-5, 10/3, (-8)/3),(10/3, (-5)/3, 5/3)]

Reqired values are

A = [(-5, 10/3, (-8)/3),(10/3, (-5)/3, 5/3)]

B = 1/3[(- 12, 2, - 16),(8, -4, 13)]

Concept: Matrices
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#### APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 11th Mathematics Volume 1 and 2 Answers Guide
Chapter 7 Matrices and Determinants
Exercise 7.1 | Q 4 | Page 18
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