Question 6: Consider the following feature vectors in \mathbb{R}^3: x…

Consider the following feature vectors in $\mathbb{R}^3$:

$x_1 = \begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}, \quad x_2 = \begin{bmatrix} -1 \\ -2 \\ 0 \end{bmatrix}, \quad x_3 = \begin{bmatrix} 3 \\ 0 \\ 1 \end{bmatrix}, \quad x_4 = \begin{bmatrix} 0 \\ 1 \\ 4 \end{bmatrix}, \quad x_5 = \begin{bmatrix} 2 \\ -1 \\ -3 \end{bmatrix}$

The labels of these points are:

$y_1 = 0, \quad y_2 = 1, \quad y_3 = 1, \quad y_4 = 0, \quad y_5 = 1$

If we use a $k$-NN algorithm with $k = 3$, what would be the predicted label for the following test point:

$x_{test} = \begin{bmatrix} 1 \\ 1 \\ 2 \end{bmatrix}$