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3 and 4 .Determinants and Matrices
medium
$a$ અને $b$ ની કઈ કિમંતો માટે આપેલ સમીકરણ સંહતીઓ $2 x+3 y+6 z=8$ ; $x+2 y+a z=5$ ; $3 x+5 y+9 z=b$ નો બીજગણ ખાલી ગણ થાય.
A
$a=3, b=13$
B
$a \neq 3, b \neq 13$
C
$a \neq 3, b=3$
D
$a=3, b \neq 13$
(JEE MAIN-2021)
Solution
$D=\left|\begin{array}{lll} 2 & 3 & 6 \\ 1 & 2 & a \\ 3 & 5 & 9 \end{array}\right|=3-a$
$D=\left|\begin{array}{lll}2 & 3 & 8 \\ 1 & 2 & 5 \\ 3 & 5 & b\end{array}\right|=b-13$
If $a=3, b \neq 13$, no solution.
Standard 12
Mathematics