<jupyter_start><jupyter_text>$$\mathbf{x} = \begin{bmatrix}1\\2\\3\\\vdots\\n\end{bmatrix}$$<jupyter_code># IGNORE
COLORS = plt.rcParams['axes.prop_cycle'].by_key()['color'] * 2

def draw_vectors(*vectors, **kwargs):
    X = np.vstack(vectors)
    fig, ax = plt.subplots()
    for i, v in enumerate(X):
        ax.arrow(0, 0, *v, color=COLORS[i], length_includes_head=True,
                 width=0.03, head_width=0.1)
    xmax, ymax = np.abs(X.max(0))
    ax.axis([-xmax - 1, xmax + 1, -ymax -1, ymax + 1])
    ax.set_aspect('equal')<jupyter_output><empty_output><jupyter_text>Vectors as Positions in Space<jupyter_code>x = np.array([1, 1])
y = np.array([1, -1])
draw_vectors(x, y)<jupyter_output><empty_output><jupyter_text>Matrices as collections of Vectors<jupyter_code>pi = np.pi

X = np.array([
    [np.cos(0),          np.sin(0)         ],
    [np.cos(pi / 4),     np.sin(pi / 4)    ],
    [np.cos(pi / 2),     np.sin(pi / 2)    ],
    [np.cos(3 * pi / 4), np.sin(3 * pi / 4)],
    [np.cos(pi),         np.sin(pi)        ],
    [np.cos(5 * pi / 4), np.sin(5 * pi / 4)],
    [np.cos(3 * pi / 2), np.sin(3 * pi / 2)],
    [np.cos(7 * pi / 4), np.sin(7 * pi / 4)]
])
draw_vectors(*X)
plt.gca().set_aspect('equal')<jupyter_output><empty_output><jupyter_text>----- Question: What is the shape of a matrix that represents 3 points on a graph paper? Exercise: Create a matrix containing any two 2D vectors which are orthogonal, and draw them with the `draw_vectors` function.<jupyter_code># enter code here<jupyter_output><empty_output>
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