A) possesses a trivial solution only
B) possesses a non-zero unique solution
C) does not have a common non-zero solution
D) has infinitely many solutions
Correct Answer: D
Solution :
Given system of equations are \[x+3y+2z=0\] \[3x+y+z=0\] and \[2x-2y-z=0\] Now, \[\Delta =\left| \begin{matrix} 1 & 3 & 2 \\ 3 & 1 & 1 \\ 2 & -2 & -1 \\ \end{matrix} \right|\] \[=1(-1+2)-3(-3-2)+2(-6-2)\] \[=1+15-16\] \[=0\] Since, determinant is zero, then it has infinitely many solutions. .You need to login to perform this action.
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