If is not invertible, then the system does not have solutions.

If for some , then is not invertible.

If the system does not have solutions, then there exists such that .

If the system has a unique solution, then is invertible.

If the system admits only one solutions.

If the system admits solutions.

If the system admits solutions.

For any the system does not admit any solution.

If the system admits only one solutions.

If the system admits solutions.

If the system admits solutions.

For any the system does not admit any solution.

For every the vectors are coplanar.

For every the vectors are linearly independent.

There exists a unique such that the vectors are linearly independent.

There does not exist a line such that and .

For all points , the triangles of vertices , and have the same area.

There exists a point such that , and are collinear.

 If , then , and are collinear.

There exists exactly two such that the points are coplanar.

 For every the points are coplanar.

There exists exactly two such that the points are collinear.

and are orthogonal for all values of . 

for all values of .

  for infinitely many values of

and are parallel for infinitely many values of . 

None of the other statements is correct.

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and intersect at exactly one point.

None of the other statements is correct.

The lines intersect at exactly one point.

The lines are skew.

The lines are parallel and distinct.

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