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The Linear Algebra Cheat Sheet by Thomas Finley is a resource that provides a concise summary of key concepts and formulas in linear algebra. It is typically used by students or individuals studying linear algebra to quickly reference important information.

Q: What is linear algebra?

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

Q: What are vectors?

A: Vectors are mathematical objects that can be added together and scaled by numbers to produce new vectors.

Q: What is a matrix?

A: A matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns.

Q: What is a system of linear equations?

A: A system of linear equations is a set of equations where the unknowns are linear.

Q: How do you solve a system of linear equations?

A: There are several methods to solve a system of linear equations, including Gaussian elimination, matrix inversion, and Cramer's rule.

Q: What is a determinant?

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

Q: What is an eigenvector?

A: An eigenvector is a non-zero vector that only changes by a scalar factor when a linear transformation is applied to it.

Q: What is a diagonal matrix?

A: A diagonal matrix is a matrix in which all the non-diagonal elements are zeros.

Q: What are eigenvalues?

A: Eigenvalues are the scalar values that are associated with the eigenvectors of a matrix.

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 dot product?

A: The dot product is a scalar operation that takes two vectors and returns a scalar.