The question asks: "What can be said about the system of vectors, if it is known that the sum of all vectors of the system equals the zero vector?"

The available answers are:

1. Among the vectors of the system, there is a zero vector.
2. Any subsystem of this vector system is linearly independent.
3. The system of vectors is linearly independent.
4. The system of vectors is linearly dependent.
5. Any subsystem of this vector system is linearly dependent.

Explanation:

If the sum of all vectors in the system equals the zero vector, it suggests that there is some linear relationship between the vectors. In other words, the system of vectors cannot be linearly independent, because a linear combination of the vectors gives the zero vector (other than the trivial case where all coefficients are zero).

Therefore, the correct answer is: "The system of vectors is linearly dependent."

Do you want further clarification or details on this?

Here are 5 related questions to consider:

1. What is the definition of linear dependence and independence?
2. How can you test if a set of vectors is linearly dependent?
3. What happens if you add a zero vector to a system of linearly independent vectors?
4. Can a set of vectors be dependent if none of them is a zero vector?
5. How does the dimensionality of the vector space affect linear independence?

Tip: A system of vectors is linearly dependent if one vector in the system can be written as a linear combination of the others.