English

If A = [(–1, 2, 3),(5, 7, 9),(–2, 1, 1)] and B = [(–4, 1, –5),(1, 2, 0),(1, 3, 1)], then verify that (A – B)' = A' – B'

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Question

If A = `[(-1, 2, 3),(5, 7, 9),(-2, 1, 1)]` and B = `[(-4, 1, -5),(1, 2, 0),(1, 3, 1)]`, then verify that (A – B)' = A' – B'

Sum
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Solution

Given, A = `[(-1, 2, 3),(5, 7, 9),(-2, 1, 1)]` and B = `[(-4, 1, -5),(1, 2, 0),(1, 3, 1)]` 

Then, (A – B) = A = `[(-1, 2, 3),(5, 7, 9),(-2, 1, 1)] - [(-4, 1, -5),(1, 2, 0),(1, 3, 1)]`

= `[(-1 + 4, 2 - 1, 3 + 5),(5 - 1, 7 - 2, 9 - 0), (-2 - 1, 1 - 3, 1 - 1)]`

= `[(3, 1, 8),(4, 5, 9),(-3, -2, 0)]`

Then, (A – B)' = `[(3, 1, 8),(4, 5, 9),(-3, -2, 0)] = [(3, 4, -3),(1, 5, -2),(8, 9, 0)] `   ...(i)

We know that, A' = `[(-1, 5, -2), (2, 7, 1),(3, 9, 1)]` and B' = `[(-4, 1, 1),(1, 2, 3),(-5, 0, 1)]`

A' – B' = `[(-1, 5, -2), (2, 7, 1),(3, 9, 1)] - [(-4, 1, 1),(1, 2, 3),(-5, 0, 1)]`

= `[(-1 + 4, 5 - 1, -2 - 1),(2 - 1, 7 - 2, 1 - 3),(3 + 5, 9 - 0, 1 - 1)]`

= `[(3, 4, -3),(1, 5, -2),(8, 9, 0)]`   ...(ii)

Equations (i) and (ii) prove that,

(A – B)' = A' – B'

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Chapter 3: Matrices - EXERCISE 3.3 [Page 66]

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NCERT Mathematics Part 1 and 2 [English] Class 12
Chapter 3 Matrices
EXERCISE 3.3 | Q 2. (ii) | Page 66

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