Consider the following matrices.
$X = \begin{bmatrix} 1 \\ 0 \\ 1 \end{bmatrix}$, $Y = \begin{bmatrix} 0 \\ 1 \\ 1 \end{bmatrix}$, $Z = \begin{bmatrix} 2 \\ -1 \\ 1 \end{bmatrix}$, $W = \begin{bmatrix} 1 \\ 1 \\ 1 \end{bmatrix}$
(a) Find scalars a and b such that Z = ax + by.
$(a, b) = \begin{pmatrix} 2, -1 \end{pmatrix}$
(b) Do there exist scalars a and b such that W = ax + by?
Yes
No
(c) If ax + by + cW = O, is it true that a = b = c = 0?
Yes
No
(d) Find scalars a, b, and c, not all equal to zero, such that ax + by + cZ = O.
$(a, b, c) = $