Question

The system $x+4y-2z=3,3x+y+5z=7$ and $2x+3y+z=5$ has:

• A. Infinite number of solutions
• B. Unique solution
• C. Trivial solution
• D. No solution

Answer 1

Answer: (D)

No solution

Determinant of coefficient matrix is,

$\Delta =\left|\begin{array}{ccc}1& 4& -2\\ 3& 1& 5\\ 2& 3& 1\end{array}\right|=1(1-15)-3(4+6)+2(20+2)=0$

And ${\Delta }_x=\left|\begin{array}{ccc}3& 4& -2\\ 7& 1& 5\\ 5& 3& 1\end{array}\right|=3(1-15)-7(4+6)+5(20+2)=-2\ne 0$

Hence no solutions (Use cramer rule )