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3 and 4 .Determinants and Matrices
hard
निम्नलिखित प्रश्न में दी गई समीकरण निकायों का संगत अथवा असंगत के रूप में वर्गीकरण कीजिए :
$5 x-y+4 z=5$ ; $2 x+3 y+5 z=2$ ; $5 x-2 y+6 z=-1$
Option A
Option B
Option C
Option D
Solution
The given system of equation is:
$5 x-y+4 z=5$
$2 x+3 y+5 z=2$
$5 x-2 y+6 z=-1$
The system of equation can be written in the form of $A X=B$, where
$A=\left[\begin{array}{ccc}5 & -1 & 4 \\ 2 & 3 & 5 \\ 3 & -2 & 6\end{array}\right], X\left[\begin{array}{l}x \\ y \\ z\end{array}\right]$ and $B=\left[\begin{array}{c}5 \\ 2 \\ -1\end{array}\right]$
Now,
$|A|=5(18+10)+1(12-25)+4(-4-15)$
$=5(28)+1(-13)+4(-19)$
$=140-13-76$
$=51 \neq 0$
$\therefore A$ is non-singular.
Therefore, $A^{-1}$ exists. Hence, the given system of equations is consistent.
Standard 12
Mathematics
