Answer: No, the given set of vectors does not form a basis for R².
Step-by-step explanation: We are given to determine whether the following set of vectors form a basis for R² or not :
S = {(1, 5), (0, 0)}.
The determinant of the matrix formed by the given vectors is

Since the determinant is zero, so the given vectors cannot be linearly independent.
Hence, they cannot form a basis for R².