Question 1174473
Let's analyze each set to determine the correct answer.

**S1 = {(1, 0, 1, 1), (1, -1, 1, 1), (0, 1, 0, 0), (1, 0, 1, 0)}**

* **Linear Independence:**
    * To check for linear independence, we can form a matrix with these vectors as rows (or columns) and calculate its determinant. If the determinant is non-zero, the vectors are linearly independent.
    * Alternatively, we can check the rank of the matrix. If the rank of the matrix is equal to the number of vectors, then the vectors are linearly independent.
    * The code provided shows that S1 is linearly dependent.
* **Spanning R4:**
    * For a set of vectors to span R4, it must have at least 4 linearly independent vectors.
    * Since S1 is linearly dependent, it cannot span R4.

**S2 = {(1, 0, 1, 2), (1, 0, 0, 0), (0, 0, 2, -1)}**

* **Linear Independence:**
    * To check for linear independence, we can form a matrix with these vectors as rows (or columns) and check its rank.
    * The code provided shows that S2 is linearly independent.
* **Spanning R4:**
    * For a set of vectors to span R4, it must have at least 4 vectors.
    * Since S2 has only 3 vectors, it cannot span R4.

**Conclusion**

* S1 is linearly dependent and does not span R4.
* S2 is linearly independent and does not span R4.

Therefore, the correct statement is:

* **S2 is linearly independent**