Write a short story (3-5 paragraphs) which only uses very simple words that a 3 year old child would likely understand. The story should use the verb ”{random.choice(verbs_list)}”, the noun ”{random.choice(nouns_list)}” and the adjective ”{random.choice(adjectives_list)}”. The story should have the following features: {random.choice(features_list)}, {random.choice(features_list)}. Remember to only use simple words!

Write a short story (3-5 paragraphs) which only uses very simple words that a 3 year old child would likely understand. The story should use the verb ”decorate”, the noun ”thunder” and the adjective ”ancient”. The story should have the following features: the story should contain at least one dialogue, the story has a bad ending. Remember to only use simple words!

Once upon a time, in an ancient house, there lived a girl named Lily. She loved to decorate her room with pretty things. One day, she found a big box in the attic. She opened it and saw many shiny decorations. Lily was very happy and decided to use them in her room. As Lily was decorating her room, the sky outside became dark. There was a loud thunder sound, and Lily got scared. She ran to her mom and said, ”Mommy, the thunder is so loud!” Her mom hugged her and said, ”Don’t worry, it will pass soon.” But the thunder did not stop. It got louder and louder, and the ancient house started to shake. Suddenly, the roof fell down on the pretty decorations. Lily was sad because her room was not pretty anymore. The end.

Summary: {a short summary generated by LLM, using the approach above}
Features: {copy the features from the initial prompt}
Sentence: {a sentence generated by LLM, which should be present in the story}
Words: {copy the words from the initial prompt}
Story:

Summary: Lily and Timmy build a sandcastle together and learn to compromise, but it gets knocked over by a gust of wind. They find beauty in the broken sandcastle and play happily with a butterfly.
Features: Dialogue, Foreshadowing, Twist
Sentence: One day, she went to the park and saw a beautiful butterfly.
Words: disagree, network, beautiful
Story:

Once upon a time, there was a little girl named Lily. She loved to play with her toys and her friends. One day, she went to the park and saw a beautiful butterfly. She tried to catch it, but it flew away. Lily’s friend, Timmy, came to play with her. They decided to build a sandcastle, but they disagreed on how to build it. Lily wanted to make it tall, while Timmy wanted to make it wide. They argued for a while, but finally agreed to make it both tall and wide. As they were building the sandcastle, they noticed a group of ants working together. They realized that the ants were building a network of tunnels. Suddenly, a gust of wind came and knocked over their sandcastle. They were sad, but then they saw the butterfly again. It landed on the remains of their sandcastle and they realized that it was still beautiful, even in its broken state. They smiled and played together happily.

Write an extract from a Computer Science textbook for a 1st-year bachelor. The coding language is Python 3.6.

This is an extract from the middle of the following topic: Singular matrices.

The extract starts with a high-level overview of the topic. Then, it presents an example and describes the solution in natural language. After that, it provides 1-2 code snippets, following the example. Each snippet has no more than 10 rows. There should be no text after code snippets.

Keep in mind that the extract should be concise and explain only one concept at a time.  The code should represent a Python function & its call. All the common ML/DS libraries are available.

Don't be too verbose. The expected length of the extract is 2 paragraphs at most.

**Singular Matrices**

In linear algebra, a matrix is termed as "singular" if it doesn't have an inverse. Another equivalent definition is when the determinant of the matrix is zero. Singular matrices are crucial because they represent systems of linear equations that do not have a unique solution.

Consider a 2x2 matrix `[[a, b], [c, d]]`. If the product of `ad` and `bc` is the same (i.e., `ad = bc`), then this matrix is singular. Let's explore this with an example: given the matrix `[[2, 4], [1, 2]]`, you'll find that the product of the diagonals yields the same result (2 * 2 = 4 * 1), thus it's a singular matrix.

import numpy as np

def is_singular(matrix):
    determinant = np.linalg.det(matrix)
    return abs(determinant) < 1e-9

matrix_example = np.array([[2, 4], [1, 2]])
print(is_singular(matrix_example))  # returns True