Values of a and b , for which system of equations 2 x+3 y+6 z=8 ; x+

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3 and 4 .Determinants and Matrices

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The values of $a$ and $b$, for which the system of equations $2 x+3 y+6 z=8$ ; $x+2 y+a z=5$ ; $3 x+5 y+9 z=b$ has no solution, are:

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

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