Answer :
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
[tex]D\\\\\\=\begin{vmatrix}1 & 5\\ 0 & 0\end{vmatrix}\\\\\\=1\times0-0\times5\\\\=0.[/tex]
Since the determinant is zero, so the given vectors cannot be linearly independent.
Hence, they cannot form a basis for R².