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

non trivial solution

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trivial solution

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infinite solutions

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no solutions

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Solution

The correct option is B
trivial solution

Once you express the given equations in the form of matrices determinant we get
$D = - 2, D_{1} = 0, D_{2} = 0, D_{3} = 0$ .
So $D \neq 0$ and $D_{1} = D_{2} = D_{3} = 0$ . So according to Cramer's rule there exists only trivial solutions and the solutions being $x = \frac{D_{1}}{D} = 0, y = \frac{D_{2}}{D} = 0, z = \frac{D_{3}}{D} = 0$

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