Question

The system of linear equations x + y = 0, x – y = 0, z = 0 will have

• A. non trivial solution
• B. a trivial solution
• C. infinite solutions
• D. no solution

Answer 1

The correct option is B a trivial solution

Once you express the given equations in the form of matrices, the determinants are $D=-2,D_1=0,D_2=0,D_3=0$. So $D\ne 0$ and $D_1=D_2=D_3=0$. So according to Cramer's rule there exists only trivial solutions and the solutions being $x=\frac{D_1}{D}=0,y=\frac{D_2}{D}=0,z=\frac{D_3}{D}=0$