Section 1: Vectors (Basics, Magnitude, Direction)

1. Define a vector and explain how it differs from a scalar using real-world examples.
2. Represent the vector from point (0, 0) to (3, 4) and describe its components.
3. Calculate the magnitude of the vector (3, 4) and explain the formula used.
4. Given vectors (2, 3) and (4, 1), perform vector addition and interpret the result.
5. Subtract the vector (1, 2) from (5, 6) and explain the geometric meaning.
6. Explain what direction means in the context of vectors and how it is represented.
7. Normalize the vector (3, 4) and explain why normalization is useful in data science.
8. Describe how vectors can represent features in a dataset with an example.

Section 2: Matrices (Structure, Rows, Columns)

1. Define a matrix and explain the meaning of rows and columns.
2. Write a 2×3 matrix and identify the number of rows and columns.
3. Explain how a dataset can be represented as a matrix with rows as observations and columns as features.
4. Identify the dimensions of a matrix with 4 rows and 5 columns.
5. Given a matrix, explain how to access a specific element using row and column indices.
6. Describe the difference between a row vector and a column vector with examples.
7. Explain how matrices are used to store tabular data in machine learning.

Section 3: Matrix Operations (Addition, Multiplication)