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3 and 4 .Determinants and Matrices
medium
The following system of linear equations $2 x+3 y+2 z=9$ ; $3 x+2 y+2 z=9$ ;$x-y+4 z=8$
A
has a solution $(\alpha, \beta, \gamma)$ satisfying $\alpha+\beta^{2}+\gamma^{3}=12$
B
has infinitely many solutions
C
does not have any solution
D
has a unique solution
(JEE MAIN-2021)
Solution
$2 x+3 y+2 z=9….(1)$
$3 x+2 y+2 z=9….(2)$
$x-y+4 z=8….(3)$
$(1)-(2) \Rightarrow-x+y=0 \Rightarrow x-y=0$
from $(3) 4 z=8 \Rightarrow z=2$
from $(1)$ $2 x+3 y=5$
$\Rightarrow x=y=1$
$\therefore$ system has unique solution
Standard 12
Mathematics
