Example TLC asks if the vector \begin{equation*} \vect{w}=\colvector{13\\15\\5\\-17\\2\\25} \end{equation*} can be written as a linear combination of the four vectors \begin{align*} \vect{u}_1&=\colvector{2\\4\\-3\\1\\2\\9}& \vect{u}_2&=\colvector{6\\3\\0\\-2\\1\\4}& \vect{u}_3&=\colvector{-5\\2\\1\\1\\-3\\0}& \vect{u}_4&=\colvector{3\\2\\-5\\7\\1\\3} \end{align*} Can it? Can any vector in $\complex{6}$ be written as a linear combination of the four vectors $\vect{u}_1,\,\vect{u}_2,\,\vect{u}_3,\,\vect{u}_4$?