I don't know where to start with this exercise:
Check if [MATH]u[/MATH] belongs to the set [MATH]C[/MATH]:
a. [MATH]u = \begin{bmatrix} -1\\ 2 \\ 1 \end{bmatrix}[/MATH] and [MATH]C = \left \{ a\begin{bmatrix} -2\\ 1 \\ 0 \end{bmatrix} + b\begin{bmatrix} 3\\ 0 \\ 1 \end{bmatrix} : a,b \in R \right \}[/MATH]
b. [MATH]u = \left ( 1,0,1 \right )[/MATH] and [MATH]C = \left \{ a_{1}(2,0,1) + a_{2}(-3,-1,1) : a_{1}, a_{2} \in R \right \}[/MATH]
Check if [MATH]u[/MATH] belongs to the set [MATH]C[/MATH]:
a. [MATH]u = \begin{bmatrix} -1\\ 2 \\ 1 \end{bmatrix}[/MATH] and [MATH]C = \left \{ a\begin{bmatrix} -2\\ 1 \\ 0 \end{bmatrix} + b\begin{bmatrix} 3\\ 0 \\ 1 \end{bmatrix} : a,b \in R \right \}[/MATH]
b. [MATH]u = \left ( 1,0,1 \right )[/MATH] and [MATH]C = \left \{ a_{1}(2,0,1) + a_{2}(-3,-1,1) : a_{1}, a_{2} \in R \right \}[/MATH]