Answer to Question #109153 in Physics for MS

Question #109153

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

Expert's answer

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

"\\begin{vmatrix}\n 1 & 1 & 1 \\\\\n 1 & -1 & 1\\\\\n0 &1 &1 \n\\end{vmatrix}=-2\\neq 0."

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

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