- generate a 1-vector of size 10
- generate a zero-matrix of size 4x3
- generate a 3x3 identity matrix
- generate 100 evenly spaced values between 7 and 9
- Form the 2-D array (without typing it in explicitly):

[[1, 6, 11],

[2, 7, 12],

[3, 8, 13],

[4, 9, 14],

[5, 10, 15]] - contruct a vector of length 100 with alternating ones and zeros ( hint: use slice indexing )
- construct a 8x8 matrix with a checkboard pattern of zeros and ones
- compute the inverse, eigenvectors and eigenvalues of the following matrix: $$\mathbf{A} = \left[\begin{array} {rrr} 6 & 4 & 9 \\ 1 & 0 & 2 \\ 3 & 1 & 1 \end{array}\right] $$

```
In [2]:
```import numpy as np

```
In [ ]:
```

The mandelbrot set is defined as the set of complex numbers $c$ for which the iteration $z_{n+1} = (z_n)^2 + c$, with $z_0=0$ does not diverge. In this exercise we want to compute the Mandelbrot set within a certain range.

- implement the function
`in_mandelbrot( real, comp )`

which computes whether a complex number (real = real part, comp=complex part) belongs to the mandelbrot set. Hint: the complex number 5+3i can be constructed in python as follows:`c = 5 + 1j*3`

. Iterate`N_max`

times and use the threshold`thresh`

. - generate a 2D array with
`1000x1000`

zeros called`M`

- compute for for all complex numbers with real part between -2 and 1 and with complex part between -1.5 and 1.5 whether they belong the Mandelbrot set and store the result in
`M`

.

```
In [6]:
```N_max = 50 # number of iterations
thresh = 50 # threshold
def in_mandelbrot( real, comp ):
# computes whether a complex number (real = real part, comp=complex part) belongs to the mandelbrot set
pass

```
In [7]:
```# plot the mandelbrot fractal
# assusmes M is a 2D array filled with boolean values
import matplotlib.pyplot as plt
plt.imshow( M)
plt.show()

```
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```

```
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```