Find the barycentric coordinates of p with respect to the affinely independent set of points that precedes it.
-$\left[ \begin{array} { r } 1 \ - 1 \ 2 \ 1 \end{array} \right] , \left[ \begin{array} { l } 2 \ 1 \ 0 \ 1 \end{array} \right] , \left[ \begin{array} { r } 1 \ 2 \ - 2 \ 0 \end{array} \right] , \mathbf { p } = \left[ \begin{array} { r } - 1 \ - 11 \ 14 \ 3 \end{array} \right]$
A) $( 4 , - 1 , - 2 )$
B) $( 5,0 , - 4 )$
C) $( 5 , - 2 , - 2 )$
D) $( 2 , - 2,1 )$

Question

Quizplus · Accepted Answer

To find the barycentric coordinates of $p$ with respect to the given points, we solve the equation $\alpha \mathbf{v}_1 + \beta \mathbf{v}_2 + \gamma \mathbf{v}_3 = \mathbf{p}$, where $\mathbf{v}_1, \mathbf{v}_2, \mathbf{v}_3$ are the given points and $\mathbf{p}$ is the point in question. The solution gives the barycentric coordinates $(\alpha, \beta, \gamma)$. The correct answer is obtained by solving this system of linear equations, which yields the barycentric coordinates $(5, -2, -2)$.

Find the Barycentric Coordinates of P with Respect to the Affinely