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3 and 4 .Determinants and Matrices
easy
સમીકરણોની સંહિતાની સુસંગતતા ચકાસો : $x+2 y=2$ ; $2 x+3 y=3$
Option A
Option B
Option C
Option D
Solution
The given system of equations is:
$x+2 y=2$
$2 x+3 y=3$
The given system of equations can be written in the form of $A X=B$, where
$A=\left[\begin{array}{ll}1 & 2 \\ 2 & 3\end{array}\right], X=\left[\begin{array}{l}2 \\ 3\end{array}\right]$ and $B=\left[\begin{array}{l}2 \\ 3\end{array}\right]$
Now,
$|A|=1(3)-2(2)=3-4=-1 \neq 0$
$\therefore A$ is non-singular.
Therefore, $A^{-1}$ exists.
Hence, the given system of equations is consistent.
Standard 12
Mathematics
