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. - Mathematics

Question

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

$A = [\begin{matrix} a + 4 3 b \\ 8 - 6 \end{matrix}] B = [\begin{matrix} 2 a + 2 b^{2} + 2 \\ 8 b^{2} - 5 b \end{matrix}]$

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

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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Equality of Matrices

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Q 21 Q 20 Q 1.1

Chapter 5: Algebra of Matrices - Exercise 5.1 [Page 8]

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Chapter 5 Algebra of Matrices
Exercise 5.1 | Q 21 | Page 8

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For What Values Of A And B If A = B, Where A=[A+43b8-6]B=[2a+2B2+28B2-5b] Disclaimer: There is a Misprint in the Question, B2 − 5b Should Be Written Instead Of B2 − 56. - Mathematics

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For What Values Of A And B If A = B, Where $A = [\begin{matrix} A + 43 b \\ 8 - 6 \end{matrix}] B = [\begin{matrix} 2 a + 2 B^{2} + 2 \\ 8 B^{2} - 5 b \end{matrix}]$ Disclaimer: There is a Misprint in the Question, B2 − 5b Should Be Written Instead Of B2 − 56. - Mathematics

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