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3 and 4 .Determinants and Matrices
medium
સુરેખ સમીકરણ સંહતિ $3 x-2 y+z=b$ ; $5 x-8 y+9 z=3$ ; $2 x+y+a z=-1$ ને એક પણ ઉકેલ ન મળે તો,તે માટેની ક્રમયુક્ત જોડ $(a,b)$એ$\dots\dots\dots$ છે.
A
$\left(3, \frac{1}{3}\right)$
B
$\left(-3, \frac{1}{3}\right)$
C
$\left(-3,-\frac{1}{3}\right)$
D
$\left(3,-\frac{1}{3}\right)$
(JEE MAIN-2022)
Solution
$\left|\begin{array}{ccc} 3 & -2 & 1 \\ 5 & -8 & 9 \\ 2 & 1 & a \end{array}\right|=0$
$3(-8 a-9)+2(5 a-18)+1(21)=0$
$\Rightarrow a=-3$
Also $\Delta_{2}=\left|\begin{array}{ccc}3 & -2 & b^{\frac{1}{3}} \\ 5 & 8 & 3 \\ 2 & 1 & -1\end{array}\right|$
If $b =\frac{1}{3}$
$\Delta_{2}=0$
So $b$ must be equal to $-\frac{1}{3}$
Standard 12
Mathematics
