Chapter 4.4, Problem 5P

Problems

Recall that three vectors . in ${ℝ}^3$ are coplanar if and only if

$\det \left(\left[v_1,v_2,v_3\right]\right)=0$

For Problem $5\text{-8}$, use this result to determine whether the given set of vectors spans ${ℝ}^3$.

$\left\{\left(1,-1,1\right),\left(2,5,3\right),\left(4,-2,1\right)\right\}$.