Insta : @inycd ( I run a club : CARD at UCLA : Catalyst for Applied Research and Development )
\[ \begin{bmatrix} 5 \\ -1 \\ 4 \end{bmatrix} = a \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} + b \begin{bmatrix} 0 \\ 1 \\ 1 \end{bmatrix} + c \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} \] \[ \begin{bmatrix} 0 & 0 & 1 & |\ \ \ \ 5\\ 0 & 1 & 1 & |-1\\ 1 & 1 & 1 & |\ \ \ \ \ 4 \end{bmatrix} \]
\[ \begin{bmatrix} 0 & 0 & 1 & |\ \ \ \ 5\\ 0 & 1 & 0 & |-6\\ 1 & 1 & 0 & | -1 \end{bmatrix} \]
\[ \begin{bmatrix} 0 & 0 & 1 & |\ \ \ \ 5\\ 0 & 1 & 0 & |-6\\ 1 & 0 & 0 & | \ \ \ \ \ 5 \end{bmatrix} \]
\[ I_{3}= \begin{bmatrix} 5 \\ -6 \\ 5 \end{bmatrix} \\ \implies \\ \vec{v}=<a,b,c> for: \\ \]
\[ \begin{bmatrix} 5 \\ -1 \\ 4 \end{bmatrix} = a \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} + b \begin{bmatrix} 0 \\ 1 \\ 1 \end{bmatrix} + c \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix} \]