JEE MAIN - Mathematics (2010 - No. 11)
Consider the system of linear equations;
$$$\matrix{
{{x_1} + 2{x_2} + {x_3} = 3} \cr
{2{x_1} + 3{x_2} + {x_3} = 3} \cr
{3{x_1} + 5{x_2} + 2{x_3} = 1} \cr
} $$$
The system has :
The system has :
exactly $$3$$ solutions
a unique solution
no solution
infinitenumber of solutions
Explanation
$$D = \left| {\matrix{
1 & 2 & 1 \cr
2 & 3 & 1 \cr
3 & 5 & 2 \cr
} } \right| = 0$$
$${D_1}\left| {\matrix{ 3 & 2 & 1 \cr 3 & 3 & 1 \cr 1 & 5 & 2 \cr } } \right| \ne 0$$
$$ \Rightarrow $$ Given system, does not have any solution.
$$ \Rightarrow $$ No solution
$${D_1}\left| {\matrix{ 3 & 2 & 1 \cr 3 & 3 & 1 \cr 1 & 5 & 2 \cr } } \right| \ne 0$$
$$ \Rightarrow $$ Given system, does not have any solution.
$$ \Rightarrow $$ No solution
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