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The question is asking about **non-singular matrices** and which of the given statements are true. Let's go through each one.

1. **In a non-singular matrix, rows are linearly dependent.**
   - **False.** In a non-singular matrix, the rows are linearly independent, which means no row can be written as a linear combination of the others.

2. **In a non-singular matrix, rows are linearly independent.**
   - **True.** By definition, a non-singular matrix has linearly independent rows. This is why its determinant is non-zero and why it has an inverse.

3. **In a non-singular matrix there is only a unique solution for the represented system of equations.**
   - **True.** A non-singular matrix implies that the corresponding system of linear equations has a unique solution because its determinant is non-zero, making the system solvable.

4. **In a non-singular matrix, one row can be a multiple of another one.**
   - **False.** If one row were a multiple of another, the rows would be linearly dependent, which contradicts the definition of a non-singular matrix.

### Correct answers:
- The second and third options are correct:
   - **In a non-singular matrix, rows are linearly independent.**
   - **In a non-singular matrix there is only a unique solution for the represented system of equations.**

Would you like more details on this? Here are some related questions to further explore this topic:

1. What is the relationship between the determinant of a matrix and its singularity?
2. How can you determine if a matrix is non-singular using Gaussian elimination?
3. What role do linearly independent vectors play in defining the rank of a matrix?
4. Can a matrix with zero rows or columns ever be non-singular?
5. How does the inverse of a matrix relate to its non-singularity?

**Tip:** A matrix is singular if its determinant is zero, meaning it does not have an inverse, and its rows or columns are linearly dependent.

Select which of the following are true for non-singular matrices:
1. In a non-singular matrix, rows are linearly dependent.
2. In a non-singular matrix, rows are linearly independent.
3. In a non-singular matrix there is only a unique solution for the represented system of equations.
4. In a non-singular matrix, one row can be a multiple of another one.

Explore the properties of non-singular matrices with this detailed explanation. Learn about linear independence, uniqueness of solutions, and why certain statements about matrix rows are true or false. This guide is perfect for students studying linear algebra at the undergraduate level.

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