To visualize the Mandelbrot set in Matplotlib, you can use the following steps:

Import the necessary libraries:
```python
import numpy as np
import matplotlib.pyplot as plt
```
Define a function to check whether a point is in the Mandelbrot set:
```python
def mandelbrot(c, max_iterations=100):
    z = 0
    n = 0
    while abs(z) <= 2 and n < max_iterations:
        z = z*z + c
        n += 1
    if n == max_iterations:
        return 0
    else:
        return n
```
The mandelbrot function takes a complex number c and a maximum number of iterations max_iterations. It returns 0 if c is in the Mandelbrot set, and the number of iterations required to escape the set otherwise.

Define the range of the complex plane that you want to plot:
```
real_range = np.linspace(-2, 1, 1000)
imag_range = np.linspace(-1, 1, 1000)
```
Here, we are defining a range of 1000 evenly spaced points between -2 and 1 on the real axis, and a range of 1000 evenly spaced points between -1 and 1 on the imaginary axis.

Use `np.meshgrid` to create a grid of complex numbers:
```python
real_part, imag_part = np.meshgrid(real_range, imag_range)
c = real_part + 1j*imag_part
```
Calculate the Mandelbrot set for each point in the grid:
```python
mandelbrot_set = np.vectorize(mandelbrot)(c)
```

Plot the Mandelbrot set using imshow:

```python
plt.imshow(mandelbrot_set.T, extent=[-2, 1, -1, 1])
plt.xlabel('Real')
plt.ylabel('Imaginary')
plt.show()
```
The extent argument sets the range of the axes, and imshow takes the transpose of the Mandelbrot set array (mandelbrot_set.T) to ensure that the axes are oriented correctly. The xlabel and ylabel functions set the labels for the axes, and show displays the plot.

Putting it all together, the complete code looks like this:
```python
import numpy as np
import matplotlib.pyplot as plt

def mandelbrot(c, max_iterations=100):
    z = 0
    n = 0
    while abs(z) <= 2 and n < max_iterations:
        z = z*z + c
        n += 1
    if n == max_iterations:
        return 0
    else:
        return n

real_range = np.linspace(-2, 1, 1000)
imag_range = np.linspace(-1, 1, 1000)

real_part, imag_part = np.meshgrid(real_range, imag_range)
c = real_part + 1j*imag_part

mandelbrot_set = np.vectorize(mandelbrot)(c)

plt.imshow(mandelbrot_set.T, extent=[-2, 1, -1, 1])
plt.xlabel('Real')
plt.ylabel('Imaginary')
plt.show()
```
When you run this code, you should see a plot of the Mandelbrot set.
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