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Algebra of Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsAlgebra of Matrices1 Mark
Question
For what values of a and b if A = B, where$\text{A}=\begin{bmatrix}\text{a}+4&3\text{b}\\8&-6\end{bmatrix},\text{ B}=\begin{bmatrix}2\text{a}+2&\text{b}^2+2\\8&\text{b}^2-5\text{b}\end{bmatrix}$
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Answer

As the given matrices A and B are equal, therefore, their corresponding elements must be equal.
Comparing the corresponding elements, we get,
$\begin{bmatrix}\text{a}+4=2\text{a}+2&3\text{b}=\text{b}^2+2\\8=8&-6=\text{b}^2-5\text{b} \end{bmatrix}$
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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