Question

Determine if the set of vectors S =(1.5).(0,0) form a basis for R2

Answer 1

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

`D\\\\\\=\begin{vmatrix}1 & 5\\ 0 & 0\end{vmatrix}\\\\\\=1*0-0*5\\\\=0.`

Since the determinant is zero, so the given vectors cannot be linearly independent.

Hence, they cannot form a basis for R².