Given x1 = 1 −1 2 and x2 = 3 1 1 .

Step 1: Determine linear independence for 4.1.1.
A set of two vectors is linearly dependent if and only if one vector is a scalar multiple of the other.
Given $x_1 = \begin{bmatrix} 1 \\ -1 \\ 2 \end{bmatrix}$ and $x_2 = \begin{bmatrix} 3 \\ 1 \\ 1 \end{bmatrix}$.
If $x_2 = k x_1$ for some scalar $k$:
From the first component: $3 = k \cdot 1 \implies k = 3$.
From the second component: $1 = k \cdot (-1) \implies k = -1$.
Since the value of $k$ is not consistent, $x