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Questions and Answers
What is the definition of an eigen vector?
What is the definition of an eigen vector?
- A vector that changes direction when a linear transformation is applied
- A vector that has the same magnitude as the original vector
- A vector that remains unchanged when a linear transformation is applied (correct)
- A vector that is perpendicular to all other vectors
What is the significance of eigen vectors in linear algebra?
What is the significance of eigen vectors in linear algebra?
- They provide a basis for understanding the behavior of a linear transformation (correct)
- They are used to solve systems of linear equations
- They are used to find the determinant of a matrix
- They are used to calculate the rank of a matrix
What is the relationship between eigen vectors and eigenvalues?
What is the relationship between eigen vectors and eigenvalues?
- Eigen vectors and eigenvalues are related through the characteristic equation of a matrix (correct)
- Eigen vectors are always the reciprocals of the corresponding eigenvalues
- Eigen vectors and eigenvalues are always orthogonal to each other
- Eigen vectors and eigenvalues are independent of each other
