Question:
If $\left[\begin{array}{cc}a-b & 2 a+c \\ 2 a-b & 3 c+d\end{array}\right]=\left[\begin{array}{cc}-1 & 5 \\ 0 & 13\end{array}\right]$, find the value of $b$
Solution:
$\left[\begin{array}{cc}a-b & 2 a+c \\ 2 a-b & 3 c+d\end{array}\right]=\left[\begin{array}{cc}-1 & 5 \\ 0 & 13\end{array}\right]$
Corresponding elements of equal matrices are equal.
$\Rightarrow a-b=-1 \quad$ and $\quad 2 a-b=0$
$\Rightarrow a-b=-1 \quad$ and $\quad 2 a=b$
$\Rightarrow a-2 a=-1 \quad$ and $\quad 2 a=b$
$\Rightarrow a=1 \quad$ and $\quad 2 a=b$
$\Rightarrow a=1 \quad$ and $\quad b=2$
Hence, the value of $b$ is 2 .
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