As the system of equations are Homogeneous the system is consistent.

Infinite solutions exist (both trivial and non-trivial solutions)

When

Let's take

When is substituted in the system of equations

(which is not possible)

Infinite non-trivial solutions does not exist.

For , lets take

Substitute in system of equations

For each pair of , we get a value of .

Therefore, for infinite non-trivial solution exists.

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