Here is another example with two consumers (A and B), two goods (X and Y):

\begin{eqnarray*} u_A(x_A, y_A) & = & \min(x_A, y_A), \ \omega_A = (1, 0) \\ u_B(x_B, y_B) & = & \min(x_B, y_B), \ \omega_B = (0, 1) \end{eqnarray*}

In this case, every feasible allocation $((x_A, y_A), (x_B, y_B))$ satisfying $y_A = x_A$ is a competitive equilibrium, and is supported by price vectors $(p_x, p_y) \in \mathbb{R}^2_+$ such that $p_xx_A +p_yy_A = p_x$ holds. In other words, every $(p_x, p_y) \in \mathbb{R}^2_+ \setminus(0,0)$ supports some allocation $((x_A, y_A), (x_B, y_B)) = \left(\left(\dfrac{p_x}{p_x+p_y}, \dfrac{p_x}{p_x+p_y}\right), \left(\dfrac{p_y}{p_x+p_y}, \dfrac{p_y}{p_x+p_y}\right)\right)$ as a completitive equilibrium.

Here is another example with two consumers (A and B), two goods (X and Y):

\begin{eqnarray*} u_A(x_A, y_A) & = & \min(x_A, y_A), \ \omega_A = (1, 0) \\ u_B(x_B, y_B) & = & \min(x_B, y_B), \ \omega_B = (0, 1) \end{eqnarray*}

In this case, every feasible allocation $((x_A, y_A), (x_B, y_B))$ satisfying $y_A = x_A$ is a competitive equilibrium, and is supported by price vectors $(p_x, p_y) \in \mathbb{R}^2_+$ such that $p_xx_A +p_yy_A = p_x$ holds. In other words, every $(p_x, p_y) \in \mathbb{R}^2_+ \setminus \{(0,0)\}$ supports some allocation i.e. $((x_A, y_A), (x_B, y_B)) = \left(\left(\dfrac{p_x}{p_x+p_y}, \dfrac{p_x}{p_x+p_y}\right), \left(\dfrac{p_y}{p_x+p_y}, \dfrac{p_y}{p_x+p_y}\right)\right)$ as a competitive equilibrium.