Solution MINM.M11 Chris Black

There are an infinite number of possible answers. We need the set of vectors \begin{align*} S &= \set{ \begin{bmatrix}1 \\ 1 \\ 0 \end{bmatrix}, \begin{bmatrix}x \\ y \\ z \end{bmatrix}, \begin{bmatrix} 1 \\ 4 \\ 5 \end{bmatrix} } \end{align*} to be linearly dependent. One way to do this by inspection is to have $\colvector{x \\ y \\ z} =\colvector{1 \\ 4 \\ 5}$. Thus, if we let $x = 1$, $y = 4$, $ z = 5$, then the matrix $A = \begin{bmatrix} 1 & 1 & 1\\ 1 & 4 & 4 \\ 0 & 5 & 5 \end{bmatrix}$ is singular.