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સમીકરણ $\left[\begin{array}{cc}a-b & 2 a+c \\ 2 a-b & 3 c+d\end{array}\right]=\left[\begin{array}{cc}-1 & 5 \\ 0 & 13\end{array}\right]$ માંથી $a,b,c$ અને $d$ તેનાં મૂલ્ય શોધો.
$a=0$, $b=2 $, $c=3$, $d=4 $
$a=1$, $b=2 $, $c=3$, $d=4 $
$a=1$, $b=2 $, $c=3$, $d=0 $
$a=1$, $b=3 $, $c=3$, $d=4 $
Solution
$\left[\begin{array}{cc}a-b & 2 a+c \\ 2 a-b & 3 c+d\end{array}\right]=\left[\begin{array}{cc}-1 & 5 \\ 0 & 13\end{array}\right]$
As the two matrices are equal, their corresponding elements are also equal. Comparing the corresponding elements, we get:
$a-b=-1$ ……….. $(1)$
$2 a-b=0$ ……….. $(2)$
$2 a+c=5$ ……….. $(3)$
$3 c+d=13$ ……….. $(4)$
From $( 2 )$, we have :
$b=2 a$
Then, from $( 1 )$, we have :
$a-2a=-1$
$\Rightarrow$ $a=1$
$\Rightarrow$ $b=2$
Now, from $(3),$ we have :
$2 \times 1+c=5$
$\Rightarrow $ $c=3$
From $(4)$ we have :
$ 3 \times 3+d=13 $
$ \Rightarrow $ $9+d=13 \Rightarrow d=4$
$\therefore $ $a=1$, $b=2 $, $c=3$, and $d=4 $
