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3 and 4 .Determinants and Matrices
medium
સમીકરણોની સંહિતાની સુસંગતતા ચકાસો : $2 x-y=5$ ; $x+y=4$
Option A
Option B
Option C
Option D
Solution
The given system of equations is:
$2 x-y=5$
$x+y=4$
The given system of equation can be written in the form of $A X=B$, where
$A=\left[\begin{array}{cc}2 & -1 \\ 1 & 1\end{array}\right], X=\left[\begin{array}{l}x \\ z\end{array}\right]$ and $B=\left[\begin{array}{l}5 \\ 4\end{array}\right]$
$|A|=2(1)-(-1)(1)=2+1=3 \neq 0$
$\therefore A$ is non-singular.
Therefore, $A^{-1}$ exists.
Hence, the given system of equations is consistent.
Standard 12
Mathematics
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