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For What Values Of A And B If A = B, Where `A = [[A + 4 3b],[8 -6]] B = [[2a +2 B^2+2],[8 B^2 - 5b]]` Disclaimer: There is a Misprint in the Question, B2 − 5b Should Be Written Instead Of B2 − 56.

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Question

For what values of a and b if A = B, where

`A = [[a + 4        3b],[8        -6]]   B = [[2a +2              b^2+2],[8                    b^2  - 5b]]`

Disclaimer: There is a misprint in the question, b2 − 5should be written instead of b2 − 56.

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Solution

​​As the given matrices A and B are equal, therefore, their corresponding elements must be equal. Comparing the corresponding elements, we get

a + 4 = 2a + 2                                 3b = b2 + 2
      8 = 8                                       −6 = b2 − 5b

On simplifying, we get

a = 2 and the common value of b = 2.

Hence, the values of a and b are 2, 2.

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Chapter 4: Algebra of Matrices - Exercise 5.1 [Page 8]

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R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 4 Algebra of Matrices
Exercise 5.1 | Q 21 | Page 8

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