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The Linear Algebra Cheatsheet from the University of Maryland is a handy resource that provides a concise summary of the key concepts and formulas in linear algebra. It is meant to help students quickly review and reference important information while studying or solving problems in the subject.

Q: What is linear algebra?

A: Linear algebra is the branch of mathematics that deals with vector spaces and linear equations.

Q: What are vectors?

A: Vectors are mathematical objects that have both magnitude and direction.

Q: What are scalar quantities?

A: Scalar quantities are mathematical objects that only have magnitude.

Q: What are matrices?

A: Matrices are rectangular arrays of numbers or symbols arranged in rows and columns.

Q: What are eigenvalues and eigenvectors?

A: Eigenvalues are scalars associated with a linear transformation and eigenvectors are the corresponding vectors.

Q: What is the determinant of a matrix?

A: The determinant of a matrix is a scalar value that can be computed from the elements of a square matrix.

Q: What is matrix multiplication?

A: Matrix multiplication is a binary operation that takes a pair of matrices and produces another matrix.

Q: What are linear transformations?

A: Linear transformations are functions that map vectors from one vector space to another while preserving certain properties.

Q: What is the rank of a matrix?

A: The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix.

Q: What is the transpose of a matrix?

A: The transpose of a matrix is formed by interchanging its rows with columns.