Answer to Question #109153 in Physics for MS

Question

Prove that set {(1,1,1),(1,-1,1),(0,1,1)} is basis for V3

Answer 1

Let us check are the vectors are not linear dependent. The triple product of vectors

$$\begin{vmatrix} 1 & 1 & 1 \\ 1 & -1 & 1\\ 0 &1 &1 \end{vmatrix}=-2\neq 0.$$

Hence, these vectors can be as a basis for $V_3$.