Linear algebra

High school (ages 12+)
Mathematics & Numbers

Name:

Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/linear-algebra

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. What is the theoretical foundation?Based on the abstract study of vector spaces and linear transformations
2. What is the key mathematical objects?Vectors, matrices, determinants, eigenvalues, eigenvectors, and subspaces
3. Why do computers use linear algebra?Computers use linear algebra to show pictures, learn from data, and find important information in big lists. It helps them do tasks like drawing, recognizing faces, and ranking web pages.
4. How do linear transformations help with pictures?Linear transformations change pictures by moving, rotating, or resizing them. They use matrices that keep the straight‑line relationships intact.

Vector Space: An abstract set of vectors closed under addition and scalar multiplication, satisfying specific algebraic properties.
Linear Map (Transformation): A function between vector spaces that preserves vector addition and scalar multiplication, represented by a matrix.
Eigenvalue and Eigenvector: Special scalars (eigenvalues) and non-zero vectors (eigenvectors) that describe how a linear transformation scales vectors without changing their direction.