Question

show that ( 1, 1, 1), ( 0, 1, 1) and ( 0, 1, -1) generate or spanned R^3

Answer 1

Given Points are,

$(1,1,1),(0,1,1),(0,1,-1)$ respectively.

Then $\Delta=\left|\begin{matrix}1&1&1\\0&1&1\\0&1&-1\\\end{matrix}\right|$

=$[1(1(-1)-(1)(1))+0+0]\\1(-1-1)=-2$

Hence $\Delta\neq 0$

So Given point generate or spanned $R^3$ .