Question

The system of equation $x+y+z=2,3x-y+2z=6$ and $3x+y+z=-18$ has

• A. unique solution
• B. no solution
• C. an infinite number of solutions
• D. zero solution as the only solution

Answer 1

Answer: (A)

unique solution

Given, the system of equations,

$x+y+z=2$

$3x-y+2z=6$

$3x+y+z=-18$

arranging the above equations in matrix form and calculating the determinant, we get,

$|A|=\left|\begin{array}{ccc}1& 1& 1\\ 3& -1& 2\\ 3& 1& 1\end{array}\right|$

$=1(-1-2)-1(3-6)+1(3+3)$

$=-3+3+6$

$=6\ne 0$

$|A|$ = determinant of coefficient matrix $\ne 0$

Therefore there exists a unique solution