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Question
If \[\begin{bmatrix}a + b & 2 \\ 5 & b\end{bmatrix} = \begin{bmatrix}6 & 5 \\ 2 & 2\end{bmatrix}\] , then find a.
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Solution
The corresponding elements of two equal matrices are equal.
\[\Rightarrow \begin{bmatrix}a + b & 2 \\ 5 & b\end{bmatrix} = \begin{bmatrix}6 & 5 \\ 2 & 2\end{bmatrix}\]
\[ \Rightarrow a + b = 6 . . . \left( 1 \right)\]
\[ \therefore b = 2\]
Putting the value of b in eq . ( 1 )
\[a + 2 = 6\]
\[ \Rightarrow a = 6 - 2\]
\[ \therefore a = 4\]
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